If the standard deviation and coefficient of variation of some observations are 1.2 and 25.6 respectively then find the mean value for the same observations ?

Concept:

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

Calculation:

Given: For some observations we have standard deviation and coefficient of variation as 1.2 and 25.6 respectively.

Here, we have to find the mean for the same observations.

Let mean be x

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

\(⇒ {\rm{Coefficient\;of\;variation}} = {\rm{}}\frac{1.2}{x} \times 100 = 25.6\)

⇒ \(x = \frac{1.2}{25.6} \times 100\)

⇒ x = 4.69 (approximately)

Hence,  option B 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.