Coefficient of Variation Formula (original) (raw)

Last Updated : 23 Jul, 2025

Coefficient of deviation in statistics is explained as the ratio of the standard deviation to the arithmetic mean, for instance, the expression standard deviation is 15 % of the arithmetic mean is the coefficient variation.

In this article, we have covered the Coefficient of Variation Definition, its related formulas, examples and others in detail.

Table of Content

What is Coefficient of Variation?

The coefficient of deviation is the dimension of comparable variability. The coefficient of deviation is the percentage of the expected deviation from the standard.

It's very useful if one wants to compare the results from two different research or tests that consist of two different results. For example, if comparing the results of two different matches that have two completely different scoring methods, like if model X has a CV of 15% and model Y has a CV of 30%, it would be conveyed that model Y has more deviation, comparable to its mean. It enables us to supply relatively simple and quick tools that help us to compare the data of different series.

Coefficient of Variation Formula

Formula to calculate the coefficient of variation is:

**Coefficient of Variation = (Standard Deviation / Mean) × 100

**In symbols: CV = (SD/x̄) × 100

Coefficient of Variation (In Finance)

It helps in the investment selection process that's why it is important in terms of finance. In the financial matrix, it shows the risk-to-reward ratio means here the standard deviation/ volatility show as the risk of the investment, and the mean is shown as the expected reward of the investment. The investors in the company identify the risk-to-reward ratio of each one of the security to develop an investment decision. In this, the low coefficient is not favourable when the average expected return is below the value of zero

The Formula for the coefficient of variation in the context of finance,

**Coefficient of Variation = σ/μ × 100%

where,

**Example for Coefficient of Variation Finance

An investor Sudhir wants to find new investments for his portfolio purpose. Where he was looking for secure investments that provides him a stable return. So, consider some of the following options for the investment.

**Standard Deviation

Standard deviation formula helps us to find the values of a particular data that is dispersed. Simply, it is defined as the deviation of the data from an average mean. In this, higher values mean that the values are far from the average mean as well as the lower values mean that values are very close to their average mean. It is said that the value of standard deviation can never be negative.

**Standard deviation is of two types

**Population Standard Deviation

**σ = √∑(X − μ)²/n

**Sample Standard Deviation

**s = √∑(X − x̄)²/n − 1

Notation for standard deviation,

**Steps for the calculation of the coefficient of variation are as follow

Examples on Coefficient of Variation Formula

**Example 1: The standard deviation and mean of the data are 8.5 and 14.5 respectively. Find the coefficient of variation.

**Solution:

SD/σ = 8.5

mean/μ = 14.5

Coefficient of variation = σ/μ × 100%

= 5.5/14.5 × 100

Coefficient of variation = 58.6%

**Example 2: The standard deviation and coefficient of variation of data are 1.4 and 26.5 respectively. Find the value of the mean.

**Solution:

C.V = 26.5

SD/σ = 1.4

Mean/x̄ = ?

C.V = σ/x̄ × 100

26.5 = 1.4 / x̄ × 100

x̄ = 1.4/26.5 × 100

x̄ = 5.28

**Example 3: If the mean and coefficient of deviation of data are 13 and 38 respectively, then locate the value of expected variation?

**Solution:

C.V = 38

SD/σ = ?

Mean/x̄ = 13

C.V = σ/x̄ × 100

38 = σ/13 × 100

σ = 13 × 38/100

σ = 4.9

**Example 4: The mean and standard variation of marks received by 40 students of a class in three subjects Mathematics, English and economics are given below.

**Subject **Mean **Standard deviation
Maths 65 10
English 60 12
Economics 57 14

**Which of the three subjects indicates the most elevated deviation and which indicates the most subordinate variation in marks?

**Solution:

Coefficient of variation for maths = σ/x̄ × 100

σ = 10.

x̄ = 65

C.V = 10/65 × 100

Coefficient of variation for maths = 15.38%

Coefficient of variation for english = σ/x̄ × 100

σ = 12

x̄ = 60

C.V = 12/60 × 100

Coefficient of variation for english = 20%

Coefficient of variation for economics = σ/x̄ × 100

σ = 14

x̄ = 57

C.V = 14/57 × 100

Coefficient of variation for economics = 24.56%

The highest variation is economics.

And the lowest variation in maths.

**Example 5: The following table gives the values of mean and friction **of heights and weights of the 10th common students of a school.

| | **Height | **Weight | | | -------------- | ------------ | -------- | | **Mean | 157 cm | 56.50 kg | | **Variance | 72.25 cm | 28.09 kg |

**Which is more varying than the other?

**Solution:

Coefficient of variation for heights

Mean x̄1 = 157cm, variance σ1² = 72. 25 cm²

Therefore standard deviation σ1 = 8. 5

Coefficient of variation

C.V1 = σ/x̄ × 100

= 8.5/157 × 100

C.V1 = 5.41% (For heights)

Coefficient of variation for weights

Mean x̄2 = 56.50kg, variance σ2² = 28.09 kg²

Therefore standard deviation σ2 = 5.3kg

Coefficient of variation

C.V1 = σ/x̄ × 100

= 5.3/56.50 × 100

C.V2 = 9.38% (For weight)

C.V1 = 5.41% and C.V2 = 9.38%

Since C .V2 > C.V1, the weight of the students is more varying than the height.

**Example 6: During a survey, 6 students were asked how many hours per day they study on average? Their answers were as follows: 3, 7, 5, 4, 3, 5. Evaluate the standard deviation.

**Solution:

Find the mean of the data:

(3 + 7 + 5 + 4 + 3 + 5)/6

= 4.5

X1 X1 - x̄ (X1 - x̄)²
3 -1.5 2.25
7 2.5 6.25
5 0.5 0.25
4 -0.5 0.25
3 -1.5 2.25
5 0.5 0.25

= 11.5

Sample standard deviation formula:

s = √∑(X − x̄)²/n − 1

= √(11.5/[6 - 1])

= √[2.3]

= 1.516

**Example 7: Four friends were comparing their scores on a recent essay. Calculate the standard deviation of their scores: 7, 3, 4, 2.

**Solution:

Find the mean of the data

(7 + 3 + 4 + 2)/4

= 4

X1 X1 - x̄ (X1 - x̄)²
7 3 9
3 -1 1
4 0 0
2 -2 4

= 14

Population standard deviation

σ = √∑(X − x̄)²/n

= √(14/[4])

= √[10]

= 3.162

Worksheet: Coefficient of Variation

Problem 1: Given the dataset: {10,12,14,16,18}. Calculate the Coefficient of Variation.

Problem 2: Given the dataset: {50,60,70,80,90}. Calculate the Coefficient of Variation.

Problem 3: Daily temperatures in degrees Celsius: {20,22,24,26,28}. Calculate the Coefficient of Variation.

Problem 4: Blood pressure readings: {120,125,130,135,140}. Calculate the Coefficient of Variation.

Problem 5: Given the dataset: {1,2,4,8,16,32}. Calculate the Coefficient of Variation.

Problem 6: Dataset 1: {6,8,10,12,14}, Dataset 2: {12,16,20,24,28}. Calculate the CV for both datasets and determine which has higher relative variability.

Problem 7: Dataset 1: {20,22,24,26,28}, Dataset 2: {30,33,36,39,42}. Calculate the CV for both datasets and determine which has higher relative variability.

Problem 8: Monthly sales figures in dollars: {1000,1500,2000,2500,3000}. Calculate the Coefficient of Variation.

Problem 9: Weights of packages in kg: {2,2.5,3,3.5,4}. Calculate the Coefficient of Variation.

Problem 10: Given the dataset: {4,8,12,16,20,24}. Calculate the Coefficient of Variation.

Summary

Coefficient of Variation (CV) is a standardized measure of the dispersion of a probability distribution or frequency distribution. It is often used to compare the degree of variation between different datasets, especially when the units of measurement differ or the means of the datasets are significantly different.