Median

The two most commonly used measures of centre in a data set are the median and mean.

The median is the middle value in a batch, so the same number of values is above and below it. (If the number of values is even, the median is defined to be half way between the two middle values.)

Mean

The mean of a data set is found by adding all the values, then dividing by the number of values, n.

The best way to understand how the mean behaves is to imagine each cross on an unjittered dot plot to be a solid object resting on a beam with negligible mass. The mean is the value at which the beam will balance.

Maths test marks

The diagram below shows the maths test mark data.

Drag the red arrow to change the value of k. When the beam is balanced, k is equal to the mean.

Mode

A third summary of centre that is occasionally encountered is the mode of the data. This is really only appropriate for discrete data and refers to the value with the highest frequency. For continuous data that are displayed in a histogram, the term modal class is sometimes used to refer to the class with highest frequency.

Median and mean in Excel

Excel has built-in functions to evaluate the median and mean of a column of marks. If the marks are contained in the cells A1 to A25 of a spreadsheet, the formula "=MEDIAN(A1:A25)" in another cell will calculate the median mark, and the formula "=AVERAGE(A1:A25)" will evaluate the mean mark.