Mean Median Mode Calculator

What mean, median, mode, and range each measure

These four statistics describe different aspects of the same dataset. The mean summarises the centre by averaging all values. The median identifies the physical middle when data are sorted. The mode finds the most common value. The range captures the spread from the smallest to the largest value.

Because they each measure something different, examining all four together is more informative than any single figure. Two datasets can share the same mean but have completely different distributions, which the median and range reveal. Understanding which measure best represents your data depends on the shape and context of the data.

Mean — arithmetic average formula

The mean is calculated by summing all values in the dataset and dividing by the number of values. It is the most widely used measure of central tendency and the basis of many statistical calculations.

Median — the middle value

The median is the value that splits a sorted dataset exactly in half. Half of the values fall below it and half above it. For an odd count of values, the median is the single middle item. For an even count, it is the average of the two middle values.

Because the median depends only on the order of values and not their magnitude, it is resistant to outliers. This makes it the preferred measure of centre when data are skewed or contain extreme values.

Mode — the most frequent value

The mode is the value that appears most often in a dataset. Unlike mean and median, a dataset can have no mode (all values unique), one mode (unimodal), or several modes (multimodal). The mode is the only measure of central tendency that can be used with categorical data such as colours, names, or labels.

In a multimodal dataset, all values that share the highest frequency are listed as modes. A bimodal distribution with two peaks, for example, signals that the data may be drawn from two distinct subgroups — an important finding that the mean alone would conceal.

Range — measuring spread

The range is the simplest measure of spread: it is the difference between the maximum and minimum values. A large range means the data are widely spread; a small range means they are clustered close together.

While range is easy to understand, it is heavily influenced by outliers because it depends solely on the two extreme values. For a more robust view of spread, standard deviation or interquartile range are better choices once you have a large or messy dataset.