Measures of central tendency - Free Essay Example

Sample details Pages: 21 Words: 6267 Downloads: 5 Date added: 2017/06/26 Category Statistics Essay Did you like this example? 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 à ¢Ã¢â€š ¬Ã‹Å"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: Don’t waste time! Our writers will create an original "Measures of central tendency" essay for you Create order 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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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, à ¢Ã¢â€š ¬Ã‹Å"x1 is one value, à ¢Ã¢â€š ¬Ã‹Å"x2 is another value in the series and the value extends upto a particular limit represented by à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"x values, using the index à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"n observations and the mean of sample is denoted by à ¢Ã¢â€š ¬Ã‹Å". Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol à ¢Ã¢â€š ¬Ã‹Å" µ, which is pronounced as à ¢Ã¢â€š ¬Ã‹Å"mue and is derived from the Greek letter à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"and can be read as à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"m and can be calculated as . ii. Assume a value from the à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 give below. Calculate the mean, median and mode of the series. 13. The mean, median and mode of a group of 85 persons were calculated as 28, 31 and 36 respectively. It was later found that while calculating these values, one value was wrongly calculated as 46 instead of the correct value 56. What will be the effect on the correction of this value on the observation? 14. Mr Sachdeva has been heading the computer department of an organization since last 7 years. Following are the year wise expenditure in Rupee for 17 years that has been spent for the maintenance of the computers. 15. Yesh Travels Limited, a travel agent is having 20 cars which are used as taxi in Greater Noida of Uttar Pradesh. The owner of the Travel agent in a surprise check asked the manager the weekly mileage records of all the 20 cars. Being the owner of the travel agent, calculate: (a) the median miles of a car traveled during the week, (b) mean mileage of the cars 16. Delhi Transport Corporation (DTC) is in news since last three months because of repeated cases of fire in its low line buses that is running from different destinations in Delhi city. The high level committee set up of by the chief minister of Delhi is in the process of investigation about the cause of the fire in buses. One of the important causes that the driver of a bus explained is the excessive speed of the buses. It is estimated that in all the routes that the buses are running requires 45 minutes. The sample data derived below shows the arrival time that had taken by some buses to their destination. Conclude from the data the reality. 17. The ages of the students pursuing their master degree in a class is given by following distribution. Estimate the modal value. 18. Calculate the arithmetic mean of the following set of data by using (a) direct method and (b) short-cut method: 19. Following is the daily wage structure of some employees who are working in M/s. Ansul Food Process on daily basis. Calculate the arithmetic mean by using (a) direct method and (b) short-cut method. 20. A candidate has attended three papers like Indian Economics (IE), Statistics (S) and econometrics (E) to clear his M.Phil degree. In each subject he has to appear a oral tests of 40 marks and written test of 60 marks. He secured 25, 21 and 18 marks in oral tests and 52, 35 and 31 marks in written tests in subjects IE, S and E respectively. You have to calculate the weighted average of marks obtained in written test taking the weights percentage of marks obtained in corresponding oral test. 21. A candidate has obtained the following percentage of marks in an examination: Business Law 65, Statistics for Managers 70, Managerial Economics 62, Business Communication 55 and Organisation Behaviour 58. The weights allocated to each subject are as 4, 1, 2, 3, and 3 respectively. Calculate the weighted mean. 22. Tata Motors Limited wanted to offer a cash gift of 7 per cent on the number of cars sold by its sales managers in Northern region of India. Calculate the mode and the median taking the average value. 23. Obtain the median and mode from the following records of a school. 24. Calculate the mean and median of the following data series: 25. Following is the temperature that is maintained in a cold storage in different seasons to preserve the vegetables. Calculate the mean and mode of the series. 26. Find the median from the following data: 27. The distribution of 2000 houses of a locality according to their distance from a petrol pump is given in the following table: 28. A housewife saves Rs. 1/- on the first day, Rs. 2/- on the second day, Rs. 3/- on third day and Rs. 31/- on the 31st day in a particular month. Calculate the mean and median of per day savings. In the amount, her husband contributes Rs. 100 on the 32nd day and Rs. 600/- on the 33rd day. Calculate the new mean and median of savings per day. 29. Compute the mode value of the following data: 30.Calculate the modal value of the following distribution. 31. The distribution of the marks obtained by 70 students of a class in a class is given below: 32. The average rainfall for a week, excluding Sunday, was 12 cms. Sunday was observed heavy rainfall for which when Sunday was included on the other days the average rose to 18 cms. Get how much rainfall was on Sunday? 33. The mean age of the combined group of men and women is 31.5 years. If the mean age of the sub-group of men is 36 years and that of the sub-group of women is 24 years, find out percentage of men and women in the group. 34. The arithmetic mean of 60 items of a series was estimated by an entrepreneur as 22. However, it was latter calculated by the auditor that an item 26 was wrongly calculated as 62. Calculate the correct mean. 35. The sales of a street ice cream seller on seven days of a week during summer season are given below. If the profit is 15% of the sales, find his average profits per day. 36.Calculate the mode of the following data: 37. Calculate the mode of the following distribution: 38. The distribution derived below reveals monthly expenditure on food items incurred by a sample of 135 families in Jalbau Bihar, a residential colony at Greater Noida. Calculate the modal value of the distribution. 39. Calculate the geometric mean of the following data: 40. A distribution is derived below. Calculate the geometric mean. 41. Calculate the geometric mean of the following distribution: 42. In between the years 2005-2009, precious metals changes rapidly in their value in the market. The total rate of return (in %) data is derived in the table below: Calculate the geometric mean of Gold, Diamond and Silver. What conclusions can one draw out of the above result? 43. The data derived below represents the battery life (in minutes) for mobile phones of different brand available in the market. Calculate the mean and median of the series. Calculate the mean deviation, standard deviation.

The Texas Revolution Essay - 1025 Words

The Texas Revolution By Jessica Bouillon Texas History The Texas Revolution was a key point in our nation’s history and in the history of the state of Texas. For, if Texas had not revolted the way that they did, it would probably not have become a state. There are many causes that are speculated on why Texas revolted whether they are political disputes against the Centralist party in Mexico that had primary control at the time of the Revolution. These and more will be explored. Also, there are key battles in the Texas Revolution that decided the final fate of Texas, none more famous than the famous Battle of San Jacinto and The Alamo. The most popular, speculated cause of the Texas Revolution is that Texas was following in the†¦show more content†¦Still another speculated cause for the revolution in Texas was economics. There were many land speculators that were also U.S. migrants to Texas that were intent on making money from selling land. They had speculators in Texas, and Coahuila and financial centers in New York and Philadelphia. The speculators would speculate how much a piece of land was worth then sell it and turn the profits over to a financial center and make a tremendous profit from it. Yet another reason why Texans might have revolted was that they were trying to preserve and maintain the political values and economic gain while under the Constitution of 1824. It gave Texas a steady population flow of American migrants moving onto Texas soil. It also gave them political liberty, freedom to own slaves and a steady economic progression. But Antonio Lopez de Santa Anna, president of Mexico, wished to impose a stricter rule which could also explain why Texas felt the need to separate from Mexico. Another speculated cause was that the Anglo-Americans that lived there refused to conform to the Mexican rules and laws. Most were protestant and therefore refused to convert to Catholicism. They also refused to pay their duties to the government and did not support troopShow MoreRelatedThe Battle Of The Texas Revolution1910 Words   |  8 PagesAmerican History takes us on the special journey back to the Texas Revolution. This battle saw a lot of heroes and also coined one of the most famous sayings in the state of Texas, â€Å"Remember the Alamo†! However, before we can get to all the guts and glory we must first look at the causes that lead to this epic revolution to understand both sides of the coin. I will look at the background, battles, people and results of the Texas Revolution, as well as give my opinion of the Mexican government’s innocenceRead MoreThe Battle Of The Texas Revolution2082 Words   |  9 PagesTexans are full of pride and have been since the term Texan was created. The Texas revolutionary war was a great battle between Mexican Republic and the Texas Colonists. The Texas Revolution was also known as the Texas War of Independence. What will be discussed throughout the research paper are the battles that took place throughout the revolutionary war. The paper will explain how these battles shaped the way Texas Independence was won and how it shaped the future for Texan colonists. The battlesRead MoreThe Texas Revolution : The Fight For Natural Rights2212 Words   |  9 PagesThe Texas Revolution: The Fight for Natural Rights Every event in history contains a cause and effect. Every cause and effect is unique in its own way. Whenever deciphering certain events in history it’s important that those researching, keep an open mind to all intertwining factors. The Texas Revolution is an important and crucial event within the history of the United States and having a full understanding of the Texas Revolution is of extreme importance to understanding Mexican-American relationsRead MoreThe Revolution Of Texas Revolution1550 Words   |  7 PagesEssay on Texas Revolution Texas Revolution, a rebellion in late 1835 and early 1836 by residents of Texas, then a part of northern Mexico, against the Mexican government and military. The rebellion led to the establishment of the independent Republic of Texas. The short-lived republic was annexed by the United States as a state in 1845. These events were among the causes of the Mexican War between the United States and Mexico, after which Mexico relinquished all claims to Texas and much of the present-dayRead MoreA Study on the Texas Revolution552 Words   |  2 PagesTexas Revolution In 1835, a small number of settlers in the territory of Texas, rebelled against the newly established government of Mexico. While they claimed that the government in Mexico had unlawfully usurped authority, establishing a tyrannical dictatorship, there were serious economic and social issues that sparked the conflict. But what is most interesting about the Texas Revolution is the relatively small numbers of soldiers involved. The Texians, as the settlers called themselves, numberedRead MoreThe Texas Revolution And The Mexican Cession738 Words   |  3 PagesThe Texas Revolution and The Mexican Cession are both significant events in our Nation’s history because it increased the size of the United States by about 500,000 square miles. It also united two different cultures and people into one unified nation. The causes of the Texas Revolution were that Texas wanted to be able to have slaves as well as representatives in the Mexican government. The Texas Revolution otherwise known as The War of Texas Independence occurred between October 1835 to AprilRead MoreWhy The Texans Were Victorious At San Jacinto1315 Words   |  6 Pages1836 in soon to be a free Texas, the weather was warm with a slight breeze on this day the 21st of April. One army fueled with rage for revenge and the other just searching for their reasons to keep marching on this far against an inferior army. The Texas revolution may have begun with the battle of Gonzales, but through sheer determination and resiliency how a ragtag army were victorious at the battle of San Jacinto. A victory which would shape the history of Mexico, Texas, United States and theRead MoreTexas Battle For Independence And Juan Seguin Essay1013 Words   |  5 PagesTexas’ Battle for Independence and Juan Seguin The battle for Texas’ independence was a hard battle. Many lives were taken, home destroyed, and families were torn apart. Texas residents wanted to break away from Mexico and become a self-governing republic inside of Mexico because they did not like Santa Anna’s laws. Mexico did not allow slave immigration, so Texas wanted to be a part of the United States that allowed slavery. But the main reason was that Mexico would not change or consider any governmentRead MoreThe State Of Texas Gained Its Independence1089 Words   |  5 PagesThe state of Texas gained its independence on December 29, 1845 after six and a half enduring months of ceaseless brawls. The colonization of Texas first began with Stephen F. Austin, whom is also recognized as the Father of Texas. Stephen began the uprising for self-reliance against the Army of Mexico, led by Antonio Là ³pez de Santa Anna, when he proposed opening up Texas to a swamp of immigrants. This action of his branched off through out the years into countless battles for the Lonestar state toRead MoreThe Mexican State Of Coahuila Y Tejas1287 Words   |  6 PagesAmerican settlement in Texas began with the encouragement of first the Spanish, and then Mexican, governments. In the summer of 1820 Moses Austin, a bankrupt 59-year old Missourian, asked Spanish authorities for a large Texas land tract which he would promote and sell to American pioneers. The request by Austin seemed preposterous. His background was that of a Philadelphia dry goods merchant, a Virginia mine operator, a Louisiana judge, and a Missouri banker. But early in 1821, the Spanish government

Tough Guise free essay sample

A response to the documentary Tough Guise by J. Katz on hegemonic masculinity. The paper reviews the documentary, Tough Guise by J. Katz on the crisis of Americas notion of masculinity. The paper discusses Katzs point that television and movie audience members are not passive recipients to the text and visuals, but instead incorporate what they see and hear into their own lives and social situations in many different ways. It shows how the effects of media and television manifest themselves in a multitude of anti-social behaviors, including the rise of hegemonic masculinity and violence in young and teenage boys. As an agent of socialization in todays society, movies play a very large role in sculpting the thoughts, opinions, and actions of children and young adults. Most movies portray men as strong, dominant, intimidating, independent, respected and in control. By doing this, we as a society are reinforcing in boys that violence is conceived to be a normal part of being men and is admired. Parents treat sons and daughters differently. Little boys are taught to be tough. When little boy’s cry their parents might respond by telling him to grow up, and be a tough. However if a little girl did the same thing she would most likely receive more sympathy from her parents. A good example of this is in athletics. It is acceptable for a female athlete to cry when an injury takes place. But male athletes are usually made fun of for being â€Å"weak† or â€Å"sissies. † These expectations can be harmful to boys and men. According to Dennis Thompson, some studies show men and women share more emotional similarities than differences. When men are forced to hold in their emotions, they are more likely to suffer from high blood pressure, and participate in riskier behaviors such as smoking or drinking. (Gender Differences in Emotional Health.   EverydayHealth. com. N. p. , n. d. Web. ) Boys and men should be allowed to grow up with non-stereotypical responses to their true emotional needs. Due to this tough guise persona, women suffer too. In the documentary â€Å"Tough Guise† Jackson Katz talks about the modern multicultural women’s movement. Katz explains how this movement in history has given men new intakes about relationships, work, and parenting. There are now many young men today who are very open minded about relationships between men and women, and sexual equality. But there has also been a â€Å"backlash. † This means some men are not adjusting to these cultural changes. For example Howard Stern plays the role of a â€Å"bad boy† who is only famous for demeaning women. Stern shows women as objects by airing them on television half naked and uses degrading names. Howard Stern makes young male viewers feel good about themselves by degrading women and regressing back to traditional sexist ways. Not only are young men seeing people like Howard Stern as the â€Å"social norm,† they are also being influenced by sexual violence films. Many slasher films show women in sexually explicit ways right before they are being assaulted. Jackson Kratz seems to think this might be why so many men are sexually assaulting women. Violence is rapid among boys and men, which is affecting our whole society. Men and boys are being bullied in their schools. This is resulting in mass murders. In order to show dominance boys and men are relying on guns. In fact, the boys interviewed felt they needed to seek revenge on those who bullied them to assert their manhood. Luke Woodham, who carried out the Pearl, Mississippi, quoted â€Å"people called me gay, stupid, fat, and lazy. Murder is not weak and slow-witted, murder is gutsy and daring. † I am not insane; I did this to show society that people like me are mistreated every day. † ( The Day Luke Woodham Killed All Those People.   YouTube. YouTube, 15 Apr. 008. )   Luke Woodham was did not fit into societies cultural norm; therefore felt the need to show his dominance by taking life’s. These are things society needs to think about. Unfortunately Men are putting up a front for society. With this being said men go through a lot in order to fit the stereotypical â€Å"manly man. † Our culture needs to see all of th e negative outcomes of putting this kind of pressure on men. Men should be allowed to be true to themselves without being judged. When men are expected to fit a certain stereotype, this sometimes results in violence against women, and society.