Question

If mean and coefficient of variation of a set of data is 10 and 5, then S.D. is​

Answer 1

$\textbf{Given:}$

$\textsf{Mean is 10}$

$\textsf{Coefficient of variation is 5}$

$\textbf{To find:}$

$\textsf{Standard deviation}$

$\textbf{Solution:}$

$\textbf{Formula used:}$

$\boxed{\mathsf{Coefficient\;of\;variation=\dfrac{S.D}{Mean}{\times}100}}$

$\implies\mathsf{5=\dfrac{S.D}{10}{\times}100}$

$\implies\mathsf{5=S.D{\times}10}$

$\implies\mathsf{S.D=\dfrac{5}{10}}$

$\implies\boxed{\mathsf{S.D=0.5}}$

Answer 2

Given : mean and coefficient of variation of data are 10 and 5%.  

To find : standard deviation

Solution:

using the formula

Coefficient of Variation = (Standard deviation /Mean) * 100 %

Coefficient of Variation  = 5%.

Mean = 10

Standard Deviation = SD

putting values in formula

=> 5  = (SD/10) * 100

=> SD =5/10  

=> SD = 0.5

standard deviation is 0.5

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