Question

If the mean of few observations is \[40\] and standard deviation is \[8\], then what is the coefficient of variation?
a). \[1\% \]
b). \[10\% \]
c). \[20\% \]
d). \[30\% \]

Answer 1

Hint: To solve this question first we assume the value of standard deviation. Then we apply the condition of the standard deviation that is the ratio of standard deviation and mean of the statistical data. On further solving that relation we get the value of standard deviation. That is our answer.

Complete step-by-step solution:
Given,
Standard deviation \[(\sigma )\] of the statistical data is
\[\sigma \] is the representation of standard deviation in statistical data
\[ \Rightarrow \sigma = 8\]
Mean \[(\mu )\] of statistical data is
\[\mu \] is the representation of mean of the statistical data
\[ \Rightarrow \mu = 40\]
To find,
Coefficient of variation \[(c.v.)\]
Formula used:
The coefficient of variation is the ratio of standard deviation to the mean of the statistical data.
\[c.v. = \dfrac{\sigma }{\mu }\]
On putting the value of \[\sigma \] and \[\mu \] in the given formula.
\[c.v. = \dfrac{8}{{40}}\]
Multiplying by 100 on the right side because the answers in the option are in percentage.
So, we have to calculate the answer in the percent.
\[c.v. = \dfrac{8}{{40}} \times 100\% \]
On calculating further.
\[c.v. = 20\% \]
Final answer:
The value of coefficient of variation of a statistical data having standard deviation of statistical data \[8\] and mean of the statistical data \[40\]is
\[ \Rightarrow c.v. = 20\% \]
Additional information:
Standard deviation: Data series around the mean of a statistical measure of data point is known as coefficient of variation
\[\sigma = \sqrt {\dfrac{{\sum {{{({x_i} - \mu )}^2}} }}{N}} \]
Here,
\[N\]= The size of the population
$x_i$ = Each value from the population
$\mu$ = The population mean
Mean: Mean of statistical data is the average of all the terms.
\[mean = \dfrac{\text{sum of total terms}}{\text{total number of terms}}\]

Note: In this question, we have to use the concept of coefficient of variation that is the ratio of the coefficient of variation that is a ratio of the standard deviation of statistical data to the mean of the statistical data. And the knowledge of standard deviation and mean of the statistical data.