Mean, Median and Mode Calculator (Average, With Working)
The mean, median, mode and range of a list of numbers, with the sorting and the sums shown.
Inputs
| Value | Times it appears |
|---|---|
| 70 | 1 |
| 79 | 1 |
| 85 | 1 |
| 88 | 1 |
| 92 | 2 |
| 94 | 1 |
- Mean working
- 88, 92, 79, 85, 92, 70, 94 add up to 600; 600 ÷ 7 = 85.7143
- Median
- 88
- Median working
- In order: 70, 79, 85, 88, 92, 92, 94. 7 values, so the median is the middle one, number 4: 88
- Mode
- 92 (appears 2 times)
- Range
- 94 − 70 = 24
- Count
- 7
- Sum
- 600
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Free embed
- Two lines of HTML, unlimited views
- Shows a small CalculateEveryday bar, with a credit link under the calculator
What each Mean, Median and Mode input means
- Numbers
- Your list, separated by commas, spaces or new lines — a spreadsheet column pastes straight in. Write 1000, not 1,000, because a comma ends a number. Enter a value as many times as it occurs, or the mean and mode will be wrong.
Mean, Median and Mode formula
mean = sum ÷ count · median = the middle value once sorted (the average of the middle two for an even count) · mode = the most frequent value
The three 'averages' answer different questions. The mean adds every value and divides by how many there are — the everyday average, pulled towards any very large or small values. The median is the middle value once the list is sorted; with an even number of values it is the average of the middle two, as OpenStax Introductory Statistics puts it. The mode is the value that appears most often, and a list can have one, several or none. The page shows the sum and division for the mean, the sorted list for the median, how often the mode appears, the range from smallest to largest, and a frequency table.
Mean, Median and Mode worked example
Seven test scores add up to 600, so the mean is 600 ÷ 7 = 85.71. Sorted — 70, 79, 85, 88, 92, 92, 94 — the fourth value is the middle one, so the median is 88. 92 appears twice, so it is the mode, and the range is 94 − 70 = 24. The low 70 drags the mean below the median.
More Mean, Median and Mode examples
Five salaries, one very large: they add up to 446,000, so the mean is 89,200 — more than any of the other four people earn. The median, the middle of 45,000, 48,000, 51,000, 52,000 and 250,000, is 51,000, a fairer picture of a typical salary. No value repeats, so there is no mode.
An even count: 3, 7, 7, 2, 9 and 4 add up to 32, so the mean is 5.3333. Sorted — 2, 3, 4, 7, 7, 9 — the middle two values are 4 and 7, so the median is 5.5. 7 appears twice, which makes it the mode.
Where the Mean, Median and Mode calculator can give the wrong answer
- With an even number of values the median is the average of the middle two: for 10, 20, 30, 40 it is 25.
- When every value appears once there is no mode; when several tie for most frequent, all are listed.
- Commas separate the numbers, so write 1000, not 1,000. The count under the result is the quickest way to catch a split number.
- One very large or small value moves the mean a lot and the median hardly at all; for incomes and house prices the median is often the fairer 'typical' figure.
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Mean, Median and Mode reference table
| Measure | Best for | Pulled by one extreme value? | For 2, 3, 4, 7, 7, 9 |
|---|---|---|---|
| Mean | Roughly symmetric data, and anything you will add up or calculate further | Yes, strongly | 5.3333 |
| Median | Skewed data: incomes, house prices, waiting times | Hardly at all | 5.5 |
| Mode | The most common value or category: shoe sizes, survey answers | No | 7 |
| Range | A quick look at the spread | Yes — it is set by the extremes | 7 |
Mean, Median and Mode FAQ
- Add them up and divide by how many there are. 4, 8, 15 and 16 sum to 43; 43 ÷ 4 = 10.75.
- Sort the numbers and take the middle one. With an even count, average the two in the middle: for 3, 5, 8, 10 the median is (5 + 8) ÷ 2 = 6.5.
- Then the data is bimodal and both are modes. 1, 1, 2, 2, 3 has modes 1 and 2. If nothing repeats, there is no mode.
- When a few extreme values would distort the mean. Nine salaries of 50,000 and one of 1,000,000 have a mean of 145,000 but a median of 50,000.
- Multiply each value by how many times it occurs, add those products, and divide by the total count. Scores of 70 (twice), 80 (five times) and 90 (three times): (140 + 400 + 270) ÷ 10 = 81. On this page you can type each value as many times as it occurs instead.
- A mean in which some values count more: multiply each by its weight, add them, and divide by the sum of the weights. A grade made of 90 (weighted 40%) and 75 (weighted 60%) is 0.4 × 90 + 0.6 × 75 = 81.