Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

<-- Previous | Newer --> | Current: 983936395 Dick Beldin at Wed, 07 Mar 2001 03:39:55 +0000.

back to [[Variance]] '''Algorithms for Calculating Variance''' The variance of a population is defined as the '''root mean squared deviation from the mean'''. That mouthful says the same as the formula below. *Variance = {(x_{1}-µ)^{2}+ (x_{2}-µ)^{2}+ ... + (x_{n}-µ)^{2}} / n; where µ is the [[Arithmetic Mean]] of the data set. There is another formula for calculating variance which you may see. It uses the sum of all the data and the sum of the squares. The formula is: *Variance = [n{x_{1}^{2}+ x_{2}^{2}+ ... + x_{n}^{2}} - {x_{1}+ x_{2}+ ... + x_{n}}^{2}] / n^{2}This formula was introduced when the prevailing calculators made it much easier to sum squares and the raw data than to sum the squared deviations. Because this formula can result in loss of precision, it should no longer be recommended except for small exercises. ---- The method of calculation may be more easily understood from the table below where the mean is 8.

i | x_{i} | x_{i}-mean | (x_{i}-mean)^{2} |

(deviation) | (squared deviation) | ||

1 | 5 | -3 | 9 |

2 | 7 | -1 | 1 |

3 | 8 | 0 | 0 |

4 | 10 | 2 | 4 |

5 | 10 | 2 | 4 |

n=5 | sum=40 | 0 | 18 |