A defense officer is appointed to train a group of soldiers who came from different regions of the country. Distribution of the soldiers belonging to different regions is as below. How can the officer find the average number of soldiers per region?



Here is the answer for his question.

Let us count the total number of soldiers i.e 6 + 4 + 7 + 3 = 20
Total number of regions = 4

Average number of soldiers per region is given by

Total number of soldiers

Total number of regions


Hence the average number of soldiers per region = 20 / 4 = 5

This type of average is called Arithmetic Mean. But it is often referred to simply as the mean. In general, the mean is given by the formula


By definition mean can be considered as the one number in the set of numbers that best describes all the numbers in that set.

In the above example we could easily calculate the mean because N (the number of regions in this case ) is very small. But if N is very large and each value in the set occurs more than once, it would be a tedious job. There is a simple way to calculate the mean for such kind of values. Let us calculate the mean for the set of values given below.


Value (X) Number of occurrences (f)
612
916
129
811
179

We can do this by adding one more column to the table which represents the product of the value and number of occurreces. Once we calculate these products we should add these products and divide it by the sum of occurences of all the values.


Value (X) Number of occurrences (f) f * X
61272
916144
129108
81188
179153

Total number of occurrences of all the values = 57
Total of the products X * f = 565
So the mean = 565 / 57 = 9.91

A general formula to calculate the mean for this kind of values is

Try to find the mean for 5, 8, 11, 5, 21, 2, 17, 8. 



                              
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