- 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.

**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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