# Mean, mode, median

Comparing different measures of the middle

mean mode median 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) 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 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) 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
random card | random quiz

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)

### related

Alcohols | Sub-atomic particles | Characters from Shakespeare's Romeo and Juliet | Nucleic acids | Biology cycles - carbon, nitrogen, water | Trigonometry |