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# Coefficient of Variation Formula

Coefficient of Variation is expressed as the ratio of standard deviation and mean. It is often abbreviated as CV. Coefficient of variation is the measure of variability of the data. When the value of coefficient of variation is higher, it means that the data has high variability and less stability. When the value of coefficient of variation is lower, it means the data has less variability and high stability.
The formula for coefficient of variation is given below:
The formula for standard deviation may vary for sample and population data type. Standard deviation formulas for sample data and population data are given below:

Where,
xi = Terms given in the data
$\bar{x}$ = Mean
n = Total number of terms.

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## Coefficient of Variation Problems

Few problems based on coefficient of variation are given below:

### Solved Examples

Question 1: Find the coefficient of variation of 5, 10, 15, 20?

Solution:

Formula for mean:

$\bar{x}$ = $\frac{\sum x}{n}$

$\bar{x}$ = $\frac{50}{4}$ = 12.5

Construct the following table:

 x $x-\bar{x}$ $(x-\bar{x})^{2}$ 5 -7.5 56.25 10 -2.5 6.25 15 2.5 6.25 20 7.5 56.25 $\sum x$ = 50 $\sum (x-\bar{x})^{2}$ = 125

Formula for population standard deviation:

S = $\sqrt{\frac{\sum (x-\bar{x})^{2}}{n}}$

= $\sqrt{\frac{125}{4}}$

= 5.59

Coefficient of variation = $\frac{Standard\ Deviation}{Mean}$

= $\frac{5.59}{12.5}$ = 0.447

Question 2: Find the coefficient of variation 100, 145, 170, 150?
Solution:

Formula for mean:

$\bar{x}$ = $\frac{\sum x}{n}$

$\bar{x}$ = $\frac{565}{4}$ = 141.25

Construct the following table:

 x $x-\bar{x}$ $(x-\bar{x})^{2}$ 100 -41.25 1701.563 145 3.75 14.063 170 28.75 826.563 150 8.75 76.563 $\sum x$ =  565 $\sum (x-\bar{x})^{2}$ =  2618.752

Formula for population standard deviation:

S = $\sqrt{\frac{\sum (x-\bar{x})^{2}}{n}}$

= $\sqrt{\frac{2618.752}{4}}$

= 25.587

Coefficient of variation = $\frac{standard\ deviation}{mean}$

= $\frac{25.587}{141.25}$ = 0.181

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