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# Variance Calculator

To find the variance, select the sample or population option, enter the comma-separated values, and click the **calculate **button using variance calculator

## Variance Calculator with steps

Variance calculator is used to find the variance of **sample **and **population **data. This variance solver also finds the standard deviation, the mean, and the statistical sum of squares in one click.

## What is a variance?

In statistics, the average of the squared deviations from the mean is said to be the **variance**. It decides whether the data values are closer or far from the average value.

The small variance tells that the random data values are closer to the mean. While the greater variance indicates that the random data values are far from the mean.

## Types of variances

- Sample variance
- Population variance

## Formulas of variance

The formula for the **population variance** is:

The formula for the **sample variance** is:

## How to calculate variance?

Follow the below examples to learn how to **calculate the variance**.

**Example 1: For sample variance**

Find the sample variance of **12, 14, 15, 19, 25**.

**Solution**

**Step 1: **First of all, **calculate the mean** of sample data.

`Mean = x̅ = Σx/n`

= [12 + 14 + 15 + 19 + 25]/5

= 85/5

**= 17**

**Step 2: **Now find the difference between each data value from the mean and the square of the differences.

Data values (x) | x_{i} - x̅ | (x_{i} - x̅)^{2} |

12 | 12 – 17 = -5 | (-5)^{2} = 25 |

14 | 14 – 17 = -3 | (-3)^{2} = 9 |

15 | 15 – 17 = -2 | (-2)^{2} = 4 |

19 | 19 – 17 = 2 | (2)^{2} = 4 |

25 | 25 – 17 = 8 | (8)^{2} = 64 |

**Step 3: **Find the statistical sum of squares.

Σ(x_{i} - x̅)^{2 }= 25 + 9 + 4 + 4 + 64

**= 106**

**Step 4:** Take the formula of **sample variance **and substitute the values.

Σ(x_{i} - x̅)^{2} / n-1 = 106/5-1

= 106/4

**= 26.5**

Try the sample variance calculator above to check the accuracy of steps and results.

**Example 2: For population variance**

Find the population variance of **10, 24, 29, 35, 36, 40**.

**Solution**

You can solve this problem by using the population variance calculator above or manually.

**Manually**

Below are the steps to solve this problem manually.

**Step 1:** First of all, **calculate the mean** of population data.

`Mean = µ = Σx/n`

= [10 + 24 + 29 + 35 + 36 + 40]/5

= 174/6

** = 29**

**Step 2: **Now find the difference between each data value from the mean and the square of the differences.

Data values (x) | x_{i} - µ | (x_{i} - µ)^{2} |

10 | 10 – 29 = -19 | (-19)^{2} = 361 |

24 | 24 – 29 = -5 | (-5)^{2} = 25 |

29 | 29 – 29 = 0 | (0)^{2} = 0 |

35 | 35 – 29 = 6 | (6)^{2} = 36 |

36 | 36 – 29 = 7 | (7)^{2} = 49 |

40 | 40 – 29 = 11 | (11)^{2} = 121 |

** Step 3: **Find the **statistical sum of squares**.

Σ(x_{i} - µ)^{2} = 361 + 25 + 0 + 36 + 49 + 121

**= 592**

**Step 4: **Take the formula of sample variance and substitute the values.

Σ(x_{i} - µ)^{2}/n = 106/6

**= 98.667**

**Using calculator**

Using the **population variance calculator** above.

**Step 1: **Select the type of **variance**.

**Step 2: **Enter the** comma-separated **values.

**Step 3: **Click the **calculate **button

The result will come in a fraction of a second.

Step-by-step solutions for variance calculations will appear as: