Mean vs Median: Which Average Should You Actually Use?

Average is doing at least three jobs in everyday speech, and picking the wrong one is how a statistic ends up technically true and completely misleading.

What each number actually measures

The mean adds everything up and divides by the count. It uses every value, which is both its strength and its weakness, because one huge number moves it a long way. The median sorts the values and takes the middle one, so it cares about position rather than size. The mode is whichever value appears most often, which is useless for salaries and genuinely useful for shoe sizes.

Run those five salaries. The mean is 40 plus 42 plus 45 plus 48 plus 300, divided by 5, which is 95, so 95,000. Four of the five earn under 50,000, barely more than half the figure being handed round as their average. The median is the third value once sorted, 45,000, and it describes the group properly. This is why national income figures are quoted as medians, and why a company advertising its average salary deserves a second look.

The one outlier test

Before you choose, ask what happens if the largest value doubles. If the answer moves a lot, the mean is fragile and the median is the safer summary. House prices, incomes, response times and donation sizes all behave that way. Exam marks, heights and daily temperatures usually do not, so the mean is fine there.

The centre is only half the story

Two datasets can share a mean and describe completely different worlds. Take 49, 50, 51 and then take 10, 50, 90. Both have a mean of 50. The sample standard deviation of the first set is 1; of the second it is 40. Reporting average 50 for both hides everything worth knowing.

Standard deviation measures typical distance from the mean, so it inherits the mean's weakness with outliers. If you went with the median because the data is skewed, quote the range or the quartiles alongside it rather than the standard deviation. Our standard deviation guide works through the formula a step at a time.

Using the statistics calculator

Paste your numbers into the box separated by commas, spaces or line breaks. A column copied straight out of a spreadsheet works, which saves retyping anything. Press calculate and you get count, sum, mean, median, mode, range, variance and standard deviation together, so mean and median sit side by side instead of needing two separate tools.

Sample or population

The toggle changes the divisor. Population divides by n, and it is right when your numbers are the entire group, such as every pupil in one class. Sample divides by n minus 1, and it is right when the numbers stand in for something larger, such as 30 customers representing all of them. Sample always returns the slightly larger figure, and on small datasets the gap is not small: for 10, 50 and 90 the population value is 32.7 against a sample value of 40. If all you need are the three centre measures, the mean, median and mode guide covers those on their own.

Common questions

Should I report the mean or the median? Report both when they differ by much. The gap between them is itself a finding, because it tells the reader the data is skewed and in which direction.

What if there are two middle values? With an even count, average the middle two. For 40, 42, 45 and 48 the median is 42 plus 45 divided by 2, which is 43.5.

Can a dataset have no mode? Yes, when every value appears once. It can also have two, which is worth investigating, because two peaks often mean two different groups have been mixed together.

How many decimal places should I keep? One more than your input data, and no more. Averaging whole exam marks to four decimal places implies a precision the marks never had.