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# 4 its definition shall be in the form of a

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Unformatted text preview: being used in further statistical computations or processing. 94 Besides the above requisites, a good average should represent maximum characteristics of the data, its value should be nearest to the most items of the given series. Arithmetic mean or mean : Arithmetic mean or simply the mean of a variable is defined as the sum of the observations divided by the number of observations. If the variable x assumes n values x1, x2 …xn then the mean, x, is given by x + x + x + .... + xn x= 1 2 3 n n 1 = ∑ xi n i =1 This formula is for the ungrouped or raw data. Example 1 : Calculate the mean for 2, 4, 6, 8, 10 Solution: 2 + 4 + 6 + 8 + 10 5 30 = =6 5 x= Short-Cut method : Under this method an assumed or an arbitrary average (indicated by A) is used as the basis of calculation of deviations from individual values. The formula is ∑d x = A+ n where, A = the assumed mean or any value in x d = the deviation of each value from the assumed mean Example 2 : A student’ s marks in 5 subjects are 75, 68, 80, 92, 56. Find his average mark. 95 Solution: X 75 A 68 80 92 56 Total ∑d x = A+ n 31 = 68 + 5 = 68 + 6.2 = 74.2 d=x-A 7 0 12 24 -12 31 Grouped Data : The mean for grouped data is obtained from the following formula: ∑ fx x= N where x = the mid-point of individual class f = the frequency of individual class N = the sum of the frequencies or total frequencies. Short-cut method : ∑ fd ×c x = A+ N x− A where d = c A = any value in x N = total frequency c = width of the class interval Example 3: Given the following frequency distribution, calculate the arithmetic mean Marks : 64 63 62 61 60 59 Number of Students :8 18 12 9 96 7 6 Solution: X 64 63 62 61 60 59 F 8 18 12 9 7 6 fx 512 1134 744 549 420 354 60 d=x-A 2 1 0 −1 −2 −3 fd 16 18 0 −9 −14 −18 3713 -7 Direct method 3713 ∑ fx = = 61.88 N 60 Short-cut method 7 ∑ fd = 62 – x = A+ = 61.88 N 60 Example 4 : Following is the distribution of persons according to different income groups. Calculate arithmetic mean. x= Income Rs(100) Number of per...
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## This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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