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 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,

x_{i} = Terms given in the data

$\bar{x}$ = Mean

n = Total number of terms.

x

$\bar{x}$ = Mean

n = Total number of terms.

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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:

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:

Formula for population standard deviation:

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

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

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 |

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

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