Question

find the coefficient of variation of the data 18,20,15,12,25​

Answer 1

The Coefficient of variation for the given data is 1.361

Therefore Coefficient of variation=1.361

Step-by-step explanation:

Given data is 18,20,15,12,25​

Let X be the given data

Therefore X=18,20,15,12,25​

To find the Coefficient of variation for the given data :

First find the mean

$Mean=\frac{\sum X}{n}$ here n is the total number of observations

$\overline{X}=\frac{18+20+15+12+25​}{5}$

$=\frac{90}{5}$

$=18$

Therefore Mean  is $\overline{X}=18$

• Now to find the standard deviation

$\sigma=\frac{\sum (X-\overline{X})^2}{n-1}$

$\sum (X-\overline{X})^2=(18-18)^2+(20-18)^2+(15-18)^2+(12-18)^2+(25-18)^2$

$=0+2^2+(-3)^2+(-6)^2+7^2$

$=4+9+36+49$

$=98$

Therefore $\sum (X-\overline{X})^2=98$

Now the standard deviation formula becomes

$\sigma=\frac{98}{5-1}$

$=\frac{98}{4}$

$=24.5$

Therefore Standard deviation $\sigma=24.5$

Now coefficient of variation $c.v=\frac{\sigma}{\overline{X}}$

$=\frac{24.5}{18}$

$=1.361$

Therefore Coefficient of variation is 1.361.