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Problems with categorical data

The median, like the mean, applies to numerical data.

For the median, the data must be ordered.

Sometimes in introducing the median to students, ordered may be emphasised but numerical taken for granted.

Often students try to find the median of categorical data sets.


A class counted the number of cars of various colours in the staff car park.


Colour Frequency
White 10
Green 3
Yellow 5
Blue 7
Red 4


Students may order categorical value labels alphabetically and pick the middle label. For example, the colours of the cars in alphabetical order are blue, green, red, white and yellow. Therefore the 'middle' colour is red.

They may order the categorical values by frequency and look for the category with the middle frequency. For example, the frequencies of car colours in ascending order are 3 (green), 4 (red), 5 (yellow), 7 (blue) and 10 (white). Therefore the 'middle' colour is yellow.

There is teaching advice on medians and categorical data included in the drawer.

Curriculum links

Year 8: Investigate the effect of individual data values, including outliers, on the mean and median