The centre of a numerical distribution refers to the value at its “middle”. Depending on the shape of the distribution, this can refer to either the mean or median.
In perfectly symmetric distributions, the centre can be found graphically as the middle bar or datapoint.

Note: in a perfectly symmetric distribution, the mean and median are equal.

Choosing a Measure for Centre: Mean or Median

Mean should be used as the measure for the centre of symmetric distributions with no extreme values.
Median can be used as a measure for the centre regardless of shape or outliers and should be used whenever the mean cannot.

Examples

For the following histograms, assuming the precise data values are known:

The distribution on the left is symmetric, but has an outlier, and so the most appropriate measure for the centre would be the median.

The distribution on the right is symmetric and has no extreme values, and so the most appropriate measure for the centre would be the mean.

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