Question

The average run scored by a batsman in 15 cricket matches is 60 and the standard deviation of the runs is 15. Find the coefficient of variation of the runs scored by him.

Answer 1

Hint: First, we will use the formula to calculate the coefficient of variation is \[\dfrac{{{\text{Standard Deviation}} \times 100}}{{{\text{Mean}}}}\]. Apply this formula of coefficient, and then use the given conditions to find the required value.

Complete step by step answer:

We know that the average run is mean.
So, we are given that the mean is 60 and the standard deviation is 15.
We know that the formula to calculate the coefficient of variation is \[\dfrac{{{\text{Standard Deviation}} \times 100}}{{{\text{Mean}}}}\].
Substituting the value of mean and standard deviation in the above formula of the coefficient of variation, we get
\[
   \Rightarrow {\text{Coefficient of Variation}} = \dfrac{{15 \times 100}}{{60}} \\
   \Rightarrow {\text{Coefficient of Variation}} = \dfrac{{1500}}{{60}} \\
   \Rightarrow {\text{Coefficient of Variation}} = 25 \\
 \]
Hence, the coefficient of variation is 25.

Note: We need to know that the average run is the mean. We know that a standard deviation is a measure of how spread out numbers are and the coefficient of variation is a statistical measure of the relative dispersion of data point in a data series. The key point to solve this question is just to know the formula of the coefficient and then substitute value properly.