Mean Calculator

Mean calculator at a glance#

A mean calculator finds the arithmetic mean of a data set: the sum of the values divided by the number of values. Add every value, count how many there are, then divide the total by that count. The mean is the most common measure of central tendency, and is often called the average.

Worked example: take the values 4, 8, 15, 16, 23 and 42. Their sum is 108, and there are 6 values, so the mean is 108 / 6 = 18. As a formula, mean = sum of values / number of values, which here gives 108 / 6 = 18.

The mean differs from the median, which is the middle value when the data is sorted in order. The mean is pulled toward unusually large or small values, while the median is not, so the two can differ on skewed data. Enter your values in the calculator above for the exact mean, along with the sum and the count, and expect a rounded figure when the division is not exact.

Population mean vs sample mean#

The arithmetic is the same; only the data set differs. The population mean (written as the Greek letter mu) averages every member of the whole group. The sample mean (written x-bar) averages a subset you measured because the whole group is too large to reach. Both add the values and divide by the count, so a sample mean is your best estimate of the population mean when measuring everyone is not practical.

Mean, median and mode#

These are the three measures of central tendency. The mean is the average of all values. The median is the middle value once the data is sorted; with an even count it is the average of the two middle values. The mode is the value that appears most often. For a fuller comparison, see the mean, median and mode calculator.

When the mean misleads#

The mean uses every value, so a few unusually large or small ones pull it toward them. On skewed data, like incomes or house prices, the median often describes the typical case better because it ignores how extreme the outliers are. The mean also needs numeric data: you cannot average categories such as colors or names, only counts and measurements.

Mean calculator FAQ#

How do you calculate the mean of a data set?#

Add up all the values, then divide by how many values there are. For 4, 8, 15, 16, 23 and 42, the sum is 108 and the count is 6, so the mean is 108 divided by 6 = 18.

How is the median different from the mean?#

The mean is the average of every value; the median is the middle value when the data is sorted. The mean shifts toward outliers while the median does not, so on skewed data the median is often the more representative figure.

How do you find the median with an even number of values?#

Sort the values, then average the two in the middle. For 4, 8, 15 and 16, the middle pair is 8 and 15, so the median is (8 + 15) divided by 2 = 11.5.

Can a mean calculator handle categorical data?#

No. The mean only works on numbers. Categorical values such as colors, names or yes/no labels cannot be averaged; for those, count frequencies or use the mode instead.

Can it be used for population data?#

Yes. The calculation is identical for a population or a sample: sum the values and divide by the count. The labels mu and x-bar only mark whether the data is the whole group or a subset.

Does the mean work well on skewed data?#

Not always. Because it weighs every value, extreme highs or lows drag it away from the typical case. On strongly skewed data the median usually gives a better sense of the center.