The topics dispersion and variability (or variance) describes the “spread” of data in a distribution. This article explains how to compute the variance and the standard.

The first measure of dispersion to look at is the variance. Let’s look at the data set below:

X Values |

4 |

5 |

2 |

7 |

## Steps to Calculate Variance:

- Calculate mean
- Subtract each value in set from mean
- Square each number from 2)
- Sum the values from 3)
- Divide by the number of values in the set

Let’s work through these steps. First, let’s calculate the mean:

M = ∑X / n (the sum of X divided by N)

M = 4 + 5 + 2 + 7 / 4

M = 18 / 4

M = 4.5

Second, we subtract each value in the set from the mean.

X Values | X – M |

4 | -0.5 |

5 | 0.5 |

2 | 2.5 |

7 | 2.5 |

Third, we square each value.

X Values | X – M | (X – M)^{2} |

4 | -0.5 | 0.25 |

5 | 0.5 | 0.25 |

2 | -2.5 | 6.25 |

7 | 2.5 | 6.25 |

Forth, we sum the values from the third.

X Values | X – M | (X – M)^{2} |

4 | -0.5 | 0.25 |

5 | 0.5 | 0.25 |

2 | -2.5 | 6.25 |

7 | 2.5 | 6.25 |

∑ | 13 |

Finally, we divide by the number of values in the set:

Variance is 13 / 4 = 3.25

To calculate the standard deviation, you simply take the square root of the variance.

Sqrt(3.25) = 1.80

So, the standard deviation is 1.80. You can confirm this by going into Excel and using the STDEV.P formula

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