Average calculator

How the average (arithmetic mean) is calculated

The arithmetic mean is the sum of all the values divided by how many values there are. For 4, 8, 15, 16, 23 and 42, the sum is 108 and there are 6 numbers, so the mean is 108 / 6 = 18.

In everyday language, “average” and “mean” are used interchangeably. But there are other measures of the central value, such as the median and the mode, which can be more useful depending on the data.

Mean, median and mode: when to use each

The median is the value in the middle when you sort the data from smallest to largest. With an even number of values, it's the mean of the two middle ones. The mode is the value that appears most often; there can be several modes or none.

The mean is strongly affected by extreme values and the median isn't. Picture five monthly salaries: 1,500, 1,600, 1,700, 1,800 and 9,000. The mean is 3,120, a figure that looks nothing like what almost anyone in the group earns; the median, 1,700, describes the typical salary much better.

• Mean: useful when the values are similar and there are no outliers (grades, daily temperatures, times).
• Median: better when some values are far from the rest (salaries, home prices, waiting times).
• Mode: useful for knowing which value is most frequent (sizes, repeated scores, survey answers).

What a weighted average is

In a weighted average, each value counts according to its weight. Multiply each value by its weight, add up the results and divide by the sum of the weights: Σ(value × weight) / Σ(weights).

It's the usual way to work out a final grade when assignments and exams don't count equally, or an average price when you buy different quantities at different prices. Weights can be percentages, credits, units or any positive number; they don't need to add up to 100.