# Mean, mode, median

Comparing different measures of the middle

mean | mode | median | |
---|---|---|---|

description | the sum of all data divided by the number of values | the most frequent data value | middle value in a set of data (or the average of the two observations at the middle) |

example calculation | 1, 2, 2, 3, 4, 7, 9 -> 28/7 -> 4 | 1, 2, 2, 3, 4, 7, 9 -> 2 | 1, 2, 2, 3, 4, 7, 9 -> 3 |

limitation | not so useful when there are outliers in the data | some data may be "multimodal" | requires data that has a linear order (can be ranked) |

special uses | the 'average' measure people are most familiar with | can be used for 'nominal' data which has no numeric value | often good for skewed data and often more robust than other measures when there are outliers |

These three different measures of the middle or average are useful in different circumstances. If you plot the frequency of observations on a graph you will see that sometimes one measure is a better estimate than others. Different shaped frequency distributions are more suited to different measures. In a "normal (Gaussian) distribution" the mean, mode, and median are equal.

Example is from Wikipedia (https://en.wikipedia.org/wiki/Mode_(statistics)#Comparison_of_mean.2C_median_and_mode)