Marco Polo And His Travels Through Asia Essays - Marco Polo

Marco Polo And His Travels Through Asia Marco Polo and His Travels through Asia The Question I am asking in my essay is, ?Why did Marco Polo go I think his reason for exploring new lands is not because he had dreams of conquest, but because he was in fact trying to find a new trading market. Marco Polo was born in Venice, Italy in 1254. His father Niccolo was a prosperous merchant who imported luxury goods from Asia. When Marco was just six years old, his father sailed off to Istanbul(then called Constantinople) and didn't come back for nine years. Marco's mother died shortly after his 16th birthday, just before his father got back from his voyage. Two years later he set out again, this time taking his son. Marco Polo was just 17 years old when he left Venice for the first time in his life . He would nearly be 42 years of age when he saw it again. So the journey to Asia had begun. The first place the Polo's reached was lesser Armenia where Marco had begun to observe new and different kinds of people. He was not always impressed. ?In former times its gentry were esteemed expert and brave soldiers but at the present day great drinkers.? From Lesser Armenia, the Polo's traveled to Anatolia in Eastern Turkey (then called Turkomania). Here Marco marveled at the horses, mules, handsome carpets and fine skills. Next came greater Armenia where Mount Arat towered nearly eighteen thousand feet into the heavens. At the top of this mountain, Marco knew, Noah's ark finally came to rest, but there was too much snow that covered the upper slopes so that no one could climb it and search for the ark. ?No one did climb it until 1829. Those explorers did not find the ark, but later explorers found evidence of fossilized wood.? The next place the Polo's voyage took them to was Zorzania (today part of Georgia). Marco became interested at a geyser grushing oil. He noticed that people used the oil to cure rashes and skin related problems, and also burned it for light. ?The European people had forgotten this method which their ancestors would be familiar with .? In the city of Mosul, the Polo's saw the finely woven cloth still called muslin today. The Nestorian Christians that lived there especially interested Marco. ?Although Marco wrote about the city of Baghdad, it is not yet certain that the Polo's actually visited it. Still, Marco did hear many miraculous stories about the area and was eager to write about it? . Next, the Polo's arrived in Tabriz, the greatest pearl market in the world. They moved on quickly to Saba in Persia. Marco saw the tombs of the three wise men Casper, Melchior and Balthasar, who of course visited the baby Jesus. ?Marco had high Praise for Persia, including horses, donkeys, grain fruits, wild game, military equipment, beautiful embroidery done by women and young people, and turquoises(Turkish stone)? . The next place the Polo's visited was probably the biggest obstacle thus far. They entered a place in Persia overwhelmed with bandits known as ?Karaunas?. ? Karaunas scoured the country and plunder everything in their reach? . For safety's sake, the Polo's joined up with a larger caravan to travel with through the region. However, the bandits still went after the large caravan and attacked it murdering many people and others were sold into slavery. Luckily, the Polo's escaped without any harm and continued their long journey. The next part of their journey, the Polo's decided to go to the Plateau of Iran and into the city of Hormuz on the Persian Gulf. None of the Polo's particularly liked Hormuz. The summer air was poisonous. ?Marco says, sixty-five hundred soldiers were caught outside the city during a windstorm. Everyone of them suffocated. When the people of Hormuz tried to bury them, the corpses crumbled apart? . Their journey then took them across a huge salt desert whose green water was too bitter and salty to drink. They then made it to a place called Tunocain. ?In my opinion, this place has the most beautiful women in the world? said Marco. From Tunocain, the Polo's went on to

What Is Conflict Essays

What Is Conflict Essays What Is Conflict Essay What Is Conflict Essay What is Conflict? The simple meaning of conflict is basically a disagreement through which the person or people involved recognize a threat to their needs, interests or concerns. With how things are now in modern life conflicts are inevitable. Anyone can get into a conflict. Sometimes little arguments lead to an intense conflict. Also, sometimes people overcome their conflicts quickly. I believe that some conflicts can be easily resolved because it teaches people how to deal with situations like that, and leads people to think about the conflicts. It means that people learn from their mistakes. Also, if the person has enough experience about dealing with conflicts, he or she will be able to resolve it easily. For example if someone was speaking aloud and was interrupted instead of straight away starting an argument they could remind the person to respect other people when speaking. We can understand from this that because of his or her knowledge in dealing with conflicts, she was able to solve it quickly before it increase into serious fight. How we respond to conflict is in two ways, we have emotional responses which are the feelings we experience in conflict, reaching from anger and fear to depression and confusion. Emotional responses are often misunderstood, as people tend to believe that others feel the same as they do. Therefore, differing emotional responses are confusing and, at times, threatening. We also have physical responses to conflict which play an important role in our ability to meet our needs in the conflict. They include high stress levels, body tension, and increased sweat, shallow or accelerated breathing, and rapid heartbeat. These responses are similar to those we experience in high-anxiety situations, and they may be managed through stress management techniques used by many people. Establishing a calmer environment in which emotions can be managed is more likely if the physical response is addressed effectively. These are important factors into our experience during conflict, because they often tell us more about what is the true source of threat that we notice; by understanding our thoughts, feelings and physical responses to conflict, we may get better insights into the best potential solutions to the situation. One key point to understanding conflicts is seeing that each person may have a different view onto any given situation. This could also be called the role of Perception. Some of these views would be one of which, gender and sexuality. Men and women often observe situations rather differently, based on both their experiences in the world. As a result, men and women will often approach conflictive situations with differing mind-sets about the desired outcomes from the situation, as well as the set of possible solutions that may exist. Another would be Knowledge (general and situational). People respond to given conflicts on the basis of the knowledge they may have about the issue at hand. This includes specific knowledge about the situation (i. e. , Do I understand what is going on here? ) and general knowledge (i. e. , Have I experienced this type of situation before? ). Such information can influence the persons willingness to engage in efforts to manage the conflict, either reinforcing confidence to deal with the dilemma or deflating the person’s willingness to openly consider alternatives. This can decide the confidence of a person when they going into a conflict. Although it is usually best to have a minimal amount of conflicts it is useful in some place such as in organisations. In fact, conflict can be good for organizations because it encourages open-mindedness and helps avoid the trend toward group think that many organizations fall prey to. The key is learning how to manage conflict effectively so that it can serve as a catalyst, rather than a burden, to organizational improvement. Although it is often assumed that people avoid conflict, many people actually enjoy conflict to a certain degree because it can be the motivation for new thinking. Considering a different point of view which represents conflict can open up new possibilities and help to generate new ideas that might otherwise have not been considered. It is like when you are in a race you will run faster when your second rather than first because you have that person in front of you pushing you to go faster. My final point about conflict is the reason why most people tend to avoid getting into conflict. Engaging in discussion and negotiation around conflict is something we normally approach with fear and hesitation, afraid that the conversation will go worse than the conflict has gone so far. In my opinion our responses, as said earlier, are likely to to include behaviours, feelings, thoughts and physical responses. If any of these responses shows tress factors that make us reluctant to talk things out, we are more inclined to follow the pathway of avoidance, basically because where scared. In addition, consider that our society tends to reward alternative responses to conflict, rather than negotiation, people who aggressively pursue their needs, arguing rather than co-operating with a situation, are often satisfied by others who prefer to put up with this. Managers and leaders are often rewarded for their aggressive, controlling approaches to problems, rather than taking a more compassionate approach to issues that may seem less decisive to the public or their staffs. I find this to be unfair but it is my opinion on it. To conclude I believe that Conflict can be easily initiated but also easily resolved if handled in the right way or if he or she has experience. There are different responses to conflict which can lead to different outcomes of the conflict. Different people have different view on situations causing controversy between them. There can be use of conflict in organisations by making it beneficial to the person or company. Finally how I believe society sees conflict and why it is normally avoided which in my opinion it should be.

How did changes in technology affect the conduct of warfare in the Essay - 1

How did changes in technology affect the conduct of warfare in the ancient world - Essay Example Battles were primarily fought for two reasons that include defense and expansion. Egyptians had to face invasions from their neighboring dominions, while for Greeks; Persian Empire was their major threat. Raising armies and developing state of the art weaponry was essential for the survival of both the empires. The changes in the technology paved the way to glory for both the empires in their respected periods of history. The main emphasis of this discussion will be on the technological analysis of the empires from the ancient world. The New Kingdom of Egypt and the Classical Ages of Greek Empire will be discussed here in detail. It was the Seventeenth Dynasty that brought an end to the rule of Hyksos, and paved the way for the Egyptians to take charge of the land. Once the center was under the control of the Egyptians, the era of the New Kingdom commenced. Three dynasties ruled Egypt during this phase of the Ancient Egypt; they include the Eighteenth Dynasty, the Nineteenth Dynasty and the Twentieth Dynasty (McDermott, 2004). Until the Second Intermediate Period, there was no organized army of the Egyptians. During the times of war, the governors of the states were ordered by the kings to arrange men for the battle. The New Kingdom of Egypt was the era of reconstruction, innovation and expansion. During this period the Egyptian Kingdom attained its maximum size (Shaw, 1991). It was economically more stable considering the commerce and trade that brought in gold and ivory in return of the agricultural produce. Unlike, the Middle Kingdom, the New Kingdom did not focused on the common man, however, during this period the social order was kept intact. Pharaohs were once again the center of all attention, and a major chunk of man power was assigned to build new pyramids, and burial places for the kings (Healy, 1992). The reign of Hyksos over the deltas of Nile taught Egyptians a number of things. Their rule in the region inspired the future

Experience mis Assignment Example | Topics and Well Written Essays - 250 words

Experience mis - Assignment Example Again, Laudon & Laudon, (2011) argues that listening to the needs of the customers is a way of improving the market product produced by the market. Ensuring that communication between customers and the staff is enhanced offers a pathway for feedback. Creating barriers to new entry into the market is important to a business’ success (Laudon & Laudon, 2011). Using information systems, the restaurant can effectively provide barriers to any new entrants in the market. For example, the restaurant can use customer feedback to ensure that the customers remain satisfied. Customer satisfaction leads to customer loyalty and hence any new competition finds it difficult to operate effectively. On top of that, the restaurant can use its network to research on any new product that is coming up in the market. This ensures that the customers are not enticed to shift loyalty to the new entrant because the restaurant provides all the products the customers need. Therefore, the use of information systems is paramount to the restaurant’s success in blocking any new entry of

Proctor and Gambles Takeover of Gillette Case Study

Proctor and Gambles Takeover of Gillette - Case Study Example Kilts needed to ensure that the long-term profitability of Gillette continued, with three well-known brands in its portfolio it was at a disadvantage to companies like P&G which had approximately 150 major brands. To ensure sustainability and future profitability for the shareholders of Gillette he approached the merger with Lafley and P&G in 2002 originally and then subsequently in 2004. The opportunities resulting from this merger included a solid return for current shareholders as well as future profitability for P&G and Gillette as a singular business under the P&G name. Unfortunately, the problems included public reaction which was seen in media attacks following the merger in 2005 as well as the state of Massachusetts. Additionally, the possibility of losing money for shareholders if the deal turned out badly was an ever-present threat. However, the opportunities for profit and a mutually beneficial future for both companies outweighed the potential problems. Between both compa nies, there were defined market shares; P&G did not really hold a market share in razors, toothbrushes, and batteries though it did maintain a large market share in other similar products that would allow it to combine the three Gillette brands into its portfolio and profit. Gillette was more adept at marketing to men, while P&G was more adept at marketing to women. Additionally were the burgeoning foreign markets and the need for increased market shares in those areas. P&G is skilled in marketing and maintaining a significant presence in China while Gillette maintained large market shares in India and Brazil. With this evidence supporting the net benefit of a merger of interests, there does not seem to be much that could improve that.

Measures of Central Tendency

Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is Measures of Central Tendency Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is

Comparing Bennetts Hamlet with Branaghs Hamlet Essay -- comparison c

Comparing Bennett's Hamlet with Branagh's Hamlet      Ã‚  Ã‚  Ã‚   Many of Shakespeare's works have been transposed from stage to screen, none so more than Hamlet. Two of the most unique film appropriations of the play are to be found in Rodney Bennett's 1980 film and Kenneth Branagh's 1996 blockbuster. The two films share many parallels between them in both interpretation and method, however they also have marked differences in their respective approaches to the text.    Perhaps the most obvious difference between these two versions is that Branagh uses the full unabridged text whereas Bennett cuts the play down by an hour or so; Kenneth Branagh justifies his use of the full text on the BBC's website stating: "When you cut the play ... what often happens is that you compress a lot of very intense set pieces and it becomes unbearable to watch. You simply fail to take some things in because you need a breath."    Another marked difference in the two versions lies in the focus of the two films. Bennett's Hamlet focuses almost entirely on the character of Hamlet himself and the domestic tragedy that occurs around him. An example of this in the film how Derek Jacobi as Hamlet speaks directly to the camera while in soliloquy. This establishes a certain rapport between Hamlet and the viewer, as if he is speaking directly to them, this also makes the film seem more theatrical in a sense. Branagh de-centres the story from around Hamlet and focuses on the wider situation, particularly with regards to Denmark's political situation. In this appropriation Hamlet is merely one player among many. This interpretative decision is reflected in the casting of the film; Kenneth Branagh takes the title role among severa... ...rbook vol.8: Hamlet on Screen, Ed.H. Klein & D. Daphinoff, Edwin Mellen Press, 1997 Sauer, David Kennedy. `Suiting the Word to the Action: Kenneth Branagh's interpolations in Hamlet', Shakespeare Yearbook vol.8: Hamlet on Screen, Ed.H. Klein & D. Daphinoff, Edwin Mellen Press, 1997 Wilmeth, Thomas L. `Fortinbras on Film: Safe Passage for the Prince', Shakespeare Yearbook vol.8: Hamlet on Screen, Ed.H. Klein & D. Daphinoff, Edwin Mellen Press, 1997 Audio Visual Bennett, Rodney. Hamlet, Shakespeare W., BBC Education, 1980 Branagh, Kenneth. Hamlet, Shakespeare W., Castle Rock Entertainment, 1996 Internet Resources `The Filming of Hamlet - Text Interpretation'. BBC Education, 15/03/02 http://www.bbc.co.uk/education/hamlet.html `Cineaste Branagh Interview', Cineaste Film Review, 15/03/02 http://www.cineaste.com   

Characteristics of a White Collar Criminal Essay

Anyone that has taken a class or even worked a â€Å"hint† of a white collar crimes understands that Edwin H. Sutherland is responsible for coining the term. In his book, White Collar Crime, Sutherland defines white collar crime as â€Å"[a]pproximately as a crime committed by a person of respectability and high social status in the course of his occupation.† (Benson & Simpson, 2009 ) While that definition may have held true in when he made the public definition in 1939, there are many examples in modern times that would argue against Dr. Sutherland’s characterization of the white collar criminal. In her paper to the U.S. Justice Department, Cynthia Barnett explains that even though the definition of white collar crime is , â€Å"hotly contested†, there appears to be three major categories white collar crime fits into. Those crimes are categorized by either the type of offender, the type of offense and those based upon organizational structure rather than offender or offense (Barnett, 2000). Barnett’s statement alone should tell us that the characteristics of a white collar criminal may be far too long of a list to generate. According to Barnett, the Federal Bureau of Investigation (FBI) has decided to define white collar crime as â€Å"[t]hose illegal acts which are characterized by deceit, concealment, or violation of trust and which are not dependent upon the application or threat of physical force or violence. Individuals and organizations commit these acts to obtain money, property, or services; to avoid the payment or loss of money or services; or to secure personal or business advantage† (Barnett, 2000). With a slight understanding of what white collar crime is, it is important  to highlight the characteristics of the typical white collar offender in order to establish profile when conducting an investigation. Reverting to what we have learned in previous psychology classes, we know that there are dozens of traits in an individual’s personality. It is virtually impossible to narrow down exactly which one(s) produce fraudulent behavior. Obviously, there are red flags that stick out for every behavior trait. It is important for business executives to be able to recognize or have trained personnel who can recognize these traits and develop appropriate risk management plans. According to Bauwens and Egan, there are five personality traits that are common between most individuals. Rather than define them all, it is most important to note that people who possess all five traits are what many would consider as â€Å"normal†. Those who exhibit more conscientiousness and agreeableness have the most direct influence on whether executives will or will not participate in fraudulent activity (Bauwens & Egan). According to our text, there are other characteristics that the â€Å"common† white collar offender may exhibit. White collar offenders tend to be, on average, sum 10 years older than non-violent offenders who commit common crimes (Benson & Simpson, 2009). While there are probably many theories why this may be, one could conclude that business executives may spend many years working their way up the corporate ladder and into a position opportunity. Another characteristic Benson and Simpson note is that many white collar offenders are college graduates. Again, many theories are possible; it can be assumed that a higher level of education must be achieved in order to move into a position of opportunity. Finally, it is important to consider the rate of employment between white collar offenders and offenders of non-violent, common crimes. In order to commit many of the offenses that are considered white collar, the offender must be employed by or have an extremely close relationship of trust with the victim organization. Therefore, steady employment is a necessity in order for the white collar offender to be successful. For many of the non-violent common offenders, their crimes are their employment. It can be  said that when a common criminal wakes up each day and begins committing their crimes, they are actually going to work. References Barnett, C. U.S. Department of Justice, Criminal Justice Information Services (CJIS) Division. (2000). The measurement of white-collar crime using uniform crime reporting (ucr) data. Retrieved December 8, 2013, from website: http://www.fbi.gov/about-us/cjis/ucr/nibrs/nibrs_wcc.pdf Bauwens, A., & Egan, V. (n.d.). Are white-collar criminals a homogeneous or hetrogeneous group?. Home Team Journal, 91-101. Retrieved December 8, 2013, from http://www.academia.edu/832919/Personality_and_white-collar_criminals Benson, M., & Simpson, S. (2009). White-collar crime. (pp. 5-32). New York: Routledge Taylor & Francis Group.

About Affirmative Action

About Affirmative Action Free Online Research Papers Affirmative Action Essay Selina A. Griswold defines affirmative action as a set of public policies and initiatives designed to help eliminate past and present discrimination based on race, color, religion, sex, or national origin. Affirmative action is a wonderful policy, which takes initiative to correct some of the misfortunes faced by not only colored people but females, yet a common myth about affirmative action is that it stands to benefit African-Americans the most. However, the largest beneficiary of affirmative action has been Caucasian women. This is because affirmative action is designed to help break the glass ceiling, the barrier that blocks Caucasian women from moving up in the workplace, in male dominated professions. Another common misconception about affirmative action is that it goes hand in hand with quotas, when it is actually based on goals. The reason for this is because quotas are fixed numbers, and are usually abandoned after they are reached. Goals on the other hand are often exceeded and continued after they are reached, and imply something to be strived for as opposed to just a fixed number. An example of a quota is a company looking to hire 35 minority workers this year, and an example of a goal is a company striving to increase its inventory of quality minority workers. As you see, quotas have the ability to almost change the definition and aim of affirmative action, therefore in my opinion quotas should not be used when regarding affirmative action. When a company must meet affirmative action quotas, it can transform affirmative action from an act of equal opportunity into a blatant advantage for minorities and women. Take this example into perspective; A company must hire â€Å"X† amount of colored workers, and â€Å"X† amount of females. However, said company has only used word of mouth advertising, and only a small amount of qualified minorities have been informed. Now in order to meet their quota, the company must hire any minorities that apply for the job without regard for their skill level or qualifications because of a lack of suitable candidates. Without affirmative action quotas, the company would only need to hire minority workers who are accurately qualified for the job instead of fighting to meet a quota to avoid some pen alty or gain an incentive. Affirmative action also expands recruiting and training techniques. It increases recruiting techniques because when it is implemented, companies attempt to recruit from a larger pool of more diverse people. This means that said company might be forced to use different advertising methods to reach areas that they may not have before. Affirmative action expands training techniques because companies are attempting to train people from a larger range of ethnicities and skill levels, therefore the company must use more diverse methods of training to get workers to a â€Å"happy medium† of overall skill level. The analogy on page 352 is a perfect example of what affirmative action really is or at least should be. Many people make the naà ¯ve assumption that affirmative action is meant to give an advantage to any female or person of color no matter what their skill level when referring to whatever position they are attempting to fulfill. This analogy shows you that this is not true. It gives the example of a batter in baseball who when on the field is against the other nine defensive players and is otherwise alone except for his teammates on the bench. The batter represents a recipient of affirmative action, and the nine defensive players stand to represent Caucasian male candidates for the same job. The analogy then goes to mention that the batter must earn his way to base, and if he hits the ball but does not make it to first base then he is out regardless of the situation. This represents the fact that if an affirmative action recipient cannot earn his or her way to be worthy for a job then he or she will not get the job and there is nothing that affirmative action can do to stop it, equivalent to being â€Å"out† in the analogy. Finally the analogy goes on to state that in the event of a tie where it can’t be determined if the player reached first base in time, that the benefit of the doubt is given to the batter because of the nine to one odds that he faced. This is equivalent to a person of color or a female being equally qualified with a Caucasian male for a job opportunity. Affirmative action would give the person an edge over the Caucasian male because of the odds that are stacked against said person due to past or current discrimination. According to the article in â€Å"In Motion Magazine†, some Caucasian male college students did not have to go to war because of a law called college draft deferment, which basically allowed college students to avoid the draft. This is a form of affirmative action that mostly White males benefited from because most people of color could not afford to go to college, which made their deferment a lot less likely. It is also surprising how no one complained about this form of affirmative action, or when bankers, farmers, or White men of power receive these incentives and it is often looked at as an entitlement. Yet the moment that incentives were expanded to be given to colored citizens and women there was an uproar of criticism. It is also ironic that some of the same people who benefited from college deferment or social engineering have a problem when a minority receives any form of competitive advantage. How can judges in the Supreme Court be opposed to affirmative action, when there is not a single judge in that group who have not benefited from some sort of affirmative action? If an advantage for a minority is considered reverse racism, then what is an advantage for a White male considered? Part of the reason why affirmative action is such a hot topic in America is because of the way the media represents it. It has been noted over time that women are rarely well represented in reports or articles covering the topic; and there are hardly ever any instances in which there is an article reporting on the affirmative action received by Caucasian males throughout any portion of history. Much more often we see articles from accredited sources focusing merely on the African-American or Latino recipients of affirmative action. Also in many of the articles, the terms â€Å"affirmative action† and â€Å"racial preference† are used interchangeably, giving the illusion that affirmative action is not a way to give minorities a competitive advantage to stay in the proximity of White male workers, but instead a way to attempt to insure that companies employ Black and Latino workers first. It then becomes much easier to see how someone could view affirmative action as reve rse racism with such horrible representation. If affirmative action were in its true form, that is without quotas that could make it an incentive numbers based program, and with accurate media representation, I do not believe that half of the people who oppose it now still would. Therefore, I would not favor a society that did not want affirmative action when in its true form. This being because in its true form there is no aspect of affirmative action not to be desired. I believe the only way that a society could not want affirmative action in its true state would be if they were misinformed about what its true state is. In conclusion, affirmative action can be a great process aimed at correcting past mistakes. America’s only problem with it stems from its media representation, and if it were to be corrected only the strictest of nay Sayers could oppose it. The question that I now pose is how long will it be before the media finally decides to accurately cover this topic, and when that day comes will those who still oppose it attempt to come up with some other way of discrediting the process? Only time will tell. Research Papers on About Affirmative ActionMoral and Ethical Issues in Hiring New EmployeesDefinition of Export QuotasAnalysis of Ebay Expanding into AsiaTwilight of the UAWComparison: Letter from Birmingham and CritoThe Hockey GameRelationship between Media Coverage and Social andResearch Process Part OneHip-Hop is ArtOpen Architechture a white paper

The Duties And Responsibilities Of Own Role Example Essays

The Duties And Responsibilities Of Own Role Example Essays The Duties And Responsibilities Of Own Role Example Essay The Duties And Responsibilities Of Own Role Example Essay 1.1 Describe the responsibilities and duties of ain function My responsibilities as a attention worker involve giving clients personal attention, such as helping with lavation, dressing, toileting demands including catheter and convene attention. Helping with nutritionary demands such as repast planning/preparation/feeding, prompting/administering medicine, transportation, cleaning. It is my duty to guarantee that the client maintains an acceptable degree of wellness and to advance the clients well-being. It is besides my duty to guarantee that all company policies and processs are carried out and to keep records for the service delivered, along with duty for guaranting that my preparation demands are kept up-to-date so that I am at the degree of criterions required to set about my function. Finally, it is my responsibility and duty to handle clients with regard and self-respect at all times. Identify criterions that influence the manner the function is carried out The criterions I have identified that influence the manner I carry out my function as a carer working in domiciliary attention are: Care Standards Act 2000 Domiciliary Care Regulations 2002 Health and Safety at Work Act 1974 Manual Handling Operations Regulations 1992 Management of Health and Safety at Work Regulations 1999 Codes of Practice National Occupation Standards Care Quality Commission Standards These make up the criterions to follow for good working pattern within Health and Social Care. Describe ways to guarantee that personal attitudes or beliefs do non blockade the quality of work To guarantee that personal attitudes or beliefs do non blockade the quality of work carried out a carer should give themselves to excellence, develop good work moralss and be professional at all times. It may besides be possible to alter personal attitudes through farther preparation. 2. Be able to reflect on ain work activities Explain why reflecting on work activities is an of import manner to develop cognition, accomplishments and pattern Reflecting on work activities can assist a attention worker derive a better/clearer apprehension of societal, cultural, personal and historical experiences. Reflecting is larning through experience, so by considering in an orderly manner we can larn from our ain ( or others ) errors, and conversely from what we ( or others ) have done good and utilize this new cognition to assist us in future state of affairss. Therefore, contemplation can assist us to happen an consciousness of our ideas and feelings which may associate to a peculiar country of our working pattern. Therefore enabling a nexus between theory and pattern, so allow integrated acquisition. Assess how good ain cognition, accomplishments and understanding meet criterions Since get downing work in the attention industry I have undertaken a considerable sum of formal preparation, along with practical on the occupation training/learning. I now have knowledge and understanding of many wellness and societal attention policies and processs and set about my function in a professional yet empathic mode. I respect each clients diverseness and equality, guarantee a high degree of confidentiality and advance their independency and well-being by keeping a high degree of personal regard. Show the ability to reflect on work activities The ability to reflect agencies to look back on something and think about it in a logical mode. So in a work capacity reflecting on what went good, what did nt travel so good, what could be changed and why this alteration would be necessary all helps sing possible results of future client calls. For illustration, in my ain work pattern when I am on a client call I try to suit my personality to the single client and work in a manner that will enable them to interact good with me. However, sometimes the communicating is nt every bit effectual as I would trust for it to be upon working with a new client, I therefore be given to travel off and reflect on how I can alter my communicating schemes with that peculiar client and near the state of affairs from a different angle on the following visit to assist guarantee that the call runs more swimmingly on this juncture. 3. Be able to hold a personal development program Identify beginnings of support for ain acquisition and development The first point of support sing ain acquisition and development should be your line director. Between the two of you you can discourse and hold farther preparation possibilities and a personal development program which may include accessing company and perchance external preparation. Discuss options with colleagues/team members/other professionals. Finding a wise man to work aboard of, and derive farther support/skills and cognition from. Describe the procedure for holding a personal development program and who should be involved The personal development program should be created by the person and should include statements and an action program that works towards accomplishing personal ends within their calling function – this could include countries such as instruction, preparation, calling, self-improvement. This program should so be discussed with the line director to look into whether the ends are in line with the organisations outlook of the person and so regular meetings should be arranged to guarantee that the personal development program stays on an accomplishable path. Contribute to pulling up ain personal development program A personal development program is alone to each person and tailored to accommodate the person s personality and end aspirations. When developing my ain personal development program I would make the followers: Determine the strongest facets of my personality traits. Determine my ends Make a mission statement to assist me concentrate on my program Make the program, which will include how my ends will be accomplished – by interrupting them down into smaller undertakings and into timescales Keep a planner/schedule to track my advancement Re-assess and update my personal development program at regular internals as necessary. In line with regular direction assessments. 4. Be able to develop ain cognition, accomplishments and understanding Show how a acquisition activity has improved ain cognition, accomplishments and understanding I attended a one twenty-four hours dementia awareness class within my organisation, which gave me a much greater apprehension of the operation of the encephalon and the countries of the encephalon involved in different sorts of dementedness. This gave me a much greater apprehension of why clients with dementedness behave in the mode that they do and why they react as they do, which finally has enabled me to be pro-active in my actions and reactions to clients with dementedness. Show how reflecting on a state of affairs has improved ain cognition, accomplishments and understanding Actively reflecting on a peculiar state of affairs enables me to measure the pros and cons of a state of affairs that has already happened. By taking into history other peoples positions and sing from all sides in an nonsubjective manner I gain farther cognition and apprehension, which enables me to subtley change my ain mode for a good result to both myself and the client. Show how feedback from others has developed ain cognition, accomplishments and understanding Receiving feedback from directors, co-workers and clients helps me to derive a better apprehension of my strengths and failings in my occupation function. It so enables me to reflect on the remarks and act on them consequently. So, for illustration, if a co-worker should feedback that I do non work good as portion of a squad I could incorporate this remark and work on my squad edifice accomplishments. If my line director should feedback that a client has commented on my high quality of attention I will besides utilize this as a positive marker of my abilities as a attention worker. Therefore, with either positive or negative feedback it gives me an apprehension of others positions of my work and I have hence gained the cognition that will ease me with honing my accomplishments consequently.