Mean, Median & Mode Calculator

What the mean, median and mode tell you

Mean, median and mode are three ways of boiling a list of numbers down to one typical value. They answer different questions. The mean is the balance point of the data, the median is the value in the middle once the list is sorted, and the mode is the value that turns up most often. The range adds a fourth fact: how far apart the smallest and largest values are.

Looking at them side by side is more useful than relying on one. When the three sit close together the data is probably fairly symmetric. When they pull apart, the data is skewed or contains a few extreme values, and that gap is a finding in itself.

How to use the calculator

1. Enter your numbers in the box. Separate them with commas, spaces, tabs or new lines. Use a dot for decimals and a minus sign for negatives.
2. Press Calculate.
3. Read the results: Mean, Median, Mode, Range (smallest - largest) and Count of numbers. If several values tie for most frequent, the Mode row shows 0 and a separate Modes row lists them.

Two details are worth knowing. Anything in the list that is not a number is read as zero and still counted, so a stray word will drag the mean down; check your list if the result looks odd. And a semicolon is not a separator, so write 4, 7, 9 or 4 7 9 rather than 4;7;9.

The arithmetic mean

The mean is what most people call the average. Add every value and divide by how many there are.

mean = (x₁ + x₂ + … + xₙ) ÷ n

Example: the numbers 56, 61, 64, 64, 70, 73, 75, 82 and 98 add up to 643, and there are 9 of them, so the mean is 643 ÷ 9 = 71.4444. Every value contributes to the mean, which makes it sensitive to unusually large or small entries. For growth rates or ratios, the geometric mean or harmonic mean is often the better choice.

The median

Sort the list from smallest to largest. With an odd number of values the median is the one in the middle. With an even number it is the average of the two middle values.

odd n: median = value at position (n + 1) ÷ 2Even n: add the values at positions n ÷ 2 and n ÷ 2 + 1, then divide by 2.

Example: the nine scores above are already sorted, and the fifth one is 70. If the 98 were removed, eight scores remain and the two middle ones are 64 and 70, so the median becomes (64 + 70) ÷ 2 = 67. The median ignores how far the extremes are from the centre, only how many values lie on each side. See the dedicated median calculator for a step-by-step walk-through.

The mode

The mode is the value that appears most often. In the nine scores, 64 appears twice and every other score once, so the mode is 64. A list can have one mode, several modes when values tie, or effectively none when every value is different.

This calculator compares values by their whole-number part: 2.5 and 2.7 are both counted as 2, and -4.5 is counted as -4. For data with meaningful decimals, round or scale it to whole numbers first. When every value appears once, each one is listed under Modes even though, strictly speaking, there is no mode. Use the mode calculator if you only need that measure.

The range

The range tells you how spread out the data is, using only its two ends.

range = largest value − smallest value

For the nine scores that is 98 − 56 = 42. The calculator prints the two ends as 56 - 98, so you can see both. Because it uses only two values, the range says nothing about how the rest are distributed; for that, look at the variance or standard deviation.

Worked example

Nine students sat the same quiz and scored 56, 61, 64, 64, 70, 73, 75, 82 and 98. Enter them as 56 61 64 64 70 73 75 82 98 and the calculator reports:

The mean (71.4) is a little higher than the median (70) because the top score of 98 sits further above the middle than the lowest score sits below it. The gap is small here, so the class results are only mildly skewed.

Which measure should you report?

The right choice depends on the shape of the data and the question being asked.

• Mean: best for roughly symmetric data and whenever totals matter, because mean × n gives back the sum.
• Median: best for skewed data such as wages, house prices or waiting times, where a few huge values would distort the mean.
• Mode: best for the most common category or size, such as the most popular shoe size in a shop.

A quick illustration: seven annual salaries of 32,000, 35,000, 36,000, 38,000, 41,000, 44,000 and 250,000 have a mean of 476,000 ÷ 7 = 68,000 but a median of 38,000. The one very high salary lifts the mean above six of the seven people, while the median still describes a typical earner.

Common mistakes

• Taking the middle of an unsorted list instead of sorting it first.
• Forgetting to average the two middle values when the count is even.
• Reporting the mean for strongly skewed data without mentioning the median.
• Reading a missing mode as zero. A list with no repeated value has no meaningful mode.
• Mixing units in one list, for example minutes and hours, which makes every measure meaningless.

If you need the average of values that carry different importance, such as course grades with different credit weights, use the weighted mean calculator instead.