Mean, mode, median

Comparing different measures of the middle

 gcse  statistics

meanmodemedian
descriptionthe sum of all data divided by the number of valuesthe most frequent data valuemiddle value in a set of data (or the average of the two observations at the middle)
example calculation1, 2, 2, 3, 4, 7, 9 -> 28/7 -> 41, 2, 2, 3, 4, 7, 9 -> 21, 2, 2, 3, 4, 7, 9 -> 3
limitationnot so useful when there are outliers in the datasome data may be "multimodal"requires data that has a linear order (can be ranked)
special usesthe 'average' measure people are most familiar withcan be used for 'nominal' data which has no numeric valueoften 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)



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