NCERT Solutions for Class 11 Maths Exercise 15.3

Grade 11 Mathematics exercise 15.3 contains only five questions and three examples. The questions are about the application of co-efficient of variation. The formula of C.V. (co-efficient of variation) is (C.V.) = (Standard Deviation)/Mean×100. Let us take an interesting example.

There are two batsmen Sachin Tendulkar and Virender Sehwag. Suppose we are required to choose one of them for a test match. Naturally, as captain anybody would like to choose a player with greater consistency and lesser variation. Said in other words, the batman with lesser degree of co variation will be chosen. Recollect the co variation is expressed as percentage.

For two series having equal means the series with greater standard deviation/ variance shall have higher degree of variance. The variables will be highly dispersed in such a series. Example 13 is a direct question in this regard. Whereas in example 14 we are required to find the arithmetic mean given the C.V. Thus, example 14 of NCERT textbook is indirect question.

The important point to be noted in this exercise, we have to apply only one formula which is very easy. However, it is to be carefully noted whether we are required to find greater consistency or greater variability or lesser variability/ lesser consistency.

Note that greater variability is the same as lesser consistency and lesser variability is higher consistency. If a student complete the previous exercise confidently, he will find exercise 15.3 very easy to solve.

To sum up, to understand co-variation, one must be able to find out standard deviation and arithmetic mean (if they are not already given in the question). To find out standard deviation we should know how to find out square root.

If you are unable to find out square root in exact terms, try to approximate it. Coefficient of variance is an important part in statistics to find the variation or deviation. It conclude that the data is consistent or variating regularly.