# Coefficient of Variation Calculator

Enter a data set for a sample or population to calculate the coefficient of variation for the data.

## Results:

Coefficient Of Variation (CV): | |
---|---|

Expressed as a Percentage: | |

Standard Deviation (σ): | |

Mean (μ): | |

Sum of Squares (SS): | |

Population Size (N): |

### Steps to Solve the Coefficient Of Variation

#### Step One: Find the Mean

Mean (μ) = sum / population size (N)

#### Step Two: Find the Sum of Squares

Sum of Squares (SS) = ∑(x_{i} - μ)²

#### Step Three: Calculate the Standard Deviation

Standard Deviation (σ) = √SS / N

#### Step Four: Calculate the Coefficient Of Variation

CV = σ / μ

Coefficient Of Variation (CV): | |
---|---|

Coefficient Of Variation %: | |

Standard Deviation (s): | |

Mean (x̄): | |

Sum of Squares (SS): | |

Sample Size (n): |

### Steps to Solve the Coefficient Of Variation

#### Step One: Find the Mean

Mean (x̄) = sum / sample size (n)

#### Step Two: Find the Sum of Squares

Sum of Squares (SS) = ∑(x_{i} - x̄)²

#### Step Three: Calculate the Standard Deviation

Standard Deviation (s) = √SS / n - 1

#### Step Four: Calculate the Coefficient Of Variation

CV = s / x̄

## How to Calculate the Coefficient of Variation

Coefficient of variation, or just *CV*, is a measure of relative variability or dispersion of data around the mean in a sample or population. More simply, it is a ratio of the standard deviation to the mean of a data set, and it’s often used to compare the amount of variability between sets of data.

The coefficient of variation is primarily used in statistics, but it’s also used in finance to measure risk and volatility in investments and in quality assurance to audit the precision of a particular process.

### Coefficient of Variation Formula

Because the coefficient of variation is a ratio, you can find it using a standard ratio formula.

Thus, the formula to calculate the coefficient of variation (CV) is:

CV = σ / μ

**Where:**

CV = coefficient of variation

σ = standard deviation

μ = mean

The formula states that the coefficient of variation *CV* is equal to the standard deviation *σ* (pronounced sigma) divided by the mean *μ* (pronounced mu).

The coefficient of variation is often expressed as a percentage. To express CV in percent form, multiply by 100, then add a percent symbol (%).

percent form = CV × 100%

**For example,** let’s calculate the coefficient of variation given a standard deviation of 0.783 and a mean of 23.41.

CV = 0.783 / 23.41

CV = 0.0334

In this example, the coefficient of variation is equal to 0.0334.

To express CV as a percentage, multiply it by 100.

0.0334 × 100 = 3.34%

In this example, the coefficient of variation is equal to 0.0334 or 3.34%.

The coefficient of variation is actually very similar to the relative standard deviation. The only difference between these two statistical measures is that the relative standard deviation is the absolute value of the CV, so it’s always positive.