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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:
Coefficient of Variation Formula
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:
Sample Standard Deviation Formula
Population Standard Deviation Formula
Where,
xi = Terms given in the data
$\bar{x}$ = Mean
n = Total number of terms.

Related Calculators
Coefficient of Variation Calculator Coefficient Calculator
Binomial Coefficient Calculator Coefficient of Determination Calculator
 

Coefficient of Variation Problems

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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:

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:

$x-\bar{x}$
 $(x-\bar{x})^{2}$
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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