Mean, Median, Mode Calculator

Get the mean, median, mode and range of any list of numbers in one go, with the sorted list and each step shown so you can see exactly where the answer comes from.

9 values read.

Mean
5.1111
Median
5
Mode
7
Range
7
Count
9
Sum
46
±1 SD23456789
▲ mean 5.1111 · ◆ median 5 · shaded band = mean ± 1 SD (2.589 to 7.6332)

Step-by-step working

  1. Sort the values from smallest to largest2, 2, 3, 4, 5, 7, 7, 7, 9
  2. Add the values and divide by the count to get the meanx̄ = (3 + 7 + 7 + 2 + 9 + 4 + 7 + 5 + …) ÷ 9 = 46 ÷ 9 = 5.111111
  3. n = 9 is odd, so the median is the middle value (position 5)median = 5
  4. The mode is the value that appears most often7 (appears 3 times)
  5. Range = largest − smallest9 − 2 = 7
Frequency table
ValueFrequencyRelativeCumulativeCum. %
220.2222222.22%
310.1111333.33%
410.1111444.44%
510.1111555.56%
730.3333888.89%
910.11119100%

Formula mean = Σx ÷ n median = middle value of the sorted list mode = most frequent value range = max − min

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

Why the median ignores outliers

Eight quiz scores. Drag the slider to turn the last score into an outlier and watch which “average” gets pulled.

42444648505254
▲ mean 47.75 · ◆ median 47.5
Mean ▲
47.8
Median ◆
47.5
Gap
0.3

The mean uses every value’s size, so one extreme value drags it. The median only cares about order, so it stays put. That’s why house prices and incomes are reported as medians, and why a mean far from the median hints at skew or outliers.

How to find each one

  • Mean: add every value, divide by the count.
  • Median: sort the values. With an odd count, take the middle one; with an even count, average the two middle values.
  • Mode: the value that appears most often. There can be one mode, several (bimodal, multimodal), or none if no value repeats.
  • Range: largest minus smallest.

Example: 3, 7, 7, 2, 9, 4, 7, 5, 2 sorted is 2, 2, 3, 4, 5, 7, 7, 7, 9. Mean = 46 ÷ 9 ≈ 5.11, median = 5 (the 5th value), mode = 7, range = 7.

Which average should you use?

The mean uses every value, which makes it sensitive to outliers. The median depends only on order, so it resists extreme values: that is why incomes and house prices are reported as medians. The mode is the only average that works for categories (the most common eye colour). If the mean is well above the median, the data are probably skewed right; well below suggests skewed left.

Frequently asked questions

What if there are two modes?

The data are bimodal and you report both. If every value appears the same number of times, there is no mode.

How do I find the median of an even number of values?

Sort them and average the two middle values. For 4, 8, 10, 15 the median is (8 + 10) ÷ 2 = 9.

Can the mean be a number that is not in the data?

Yes, and it usually is. The mean of 1, 2, 4 is 2.33. The median of an even-sized list can also fall between data values.