If the mean and coefficient of variation of a data set are 25.6 and 18.75 respectively then find the standard deviation for the same data set.

Concept:

\({\rm{Coefficient\;of\;variation}} = {\rm{}}\frac{{{\rm{standard\;deviaiton}}}}{{{\rm{Mean}}}} \times 100\)

Calculation:

Given: For a data set the mean and coefficient of variation are 25.6 and 18.75 respectively

Here, we have to find the standard deviation for the same observations.

Let the standard deviation be x

As we know, \({\rm{Coefficient\;of\;variation}} = {\rm{}}\frac{{{\rm{standard\;deviaiton}}}}{{{\rm{Mean}}}} \times 100\)

\(⇒ {\rm{Coefficient\;of\;variation}} = {\rm{}}\frac{x}{25.6} \times 100 = 18.75\)

⇒ \(x = \frac{18.75 \times 25.6}{100}\)

⇒ x = 4.8

Hence,  option A is the correct answer.

Adding a constant to each value: The median, mean, and quartiles will be changed by adding a constant to each value. However, the range, interquartile range, standard deviation and variance will remain the same.

Multiplying every value by a constant: however, will multiply the mean, median, quartiles, range, interquartile range, and standard deviation by that constant, and multiply the variance by the square of that constant.