Mean, Median and Mode Calculator
Type or paste a list of numbers to get the mean, median, mode and range, with each one worked out step by step.
Separate them with commas, spaces or new lines; paste a column from a spreadsheet.
Mean (average)
7
For these 10 values the mean is 7, the median 7 and the mode 7.
- Median
- 7
- Mode
- 7 (×3)
- Range
- 9 (3 to 12)
How to find the mean, median and mode
The mean (the everyday “average”) is the total divided by how many values there are. For 7, 3, 9, 4, 7, 12, 5, 7, 6 and 10 the total is 70 and there are 10 values, so the mean is 7.
The median is the middle value once the data are sorted: 3, 4, 5, 6, 7, 7, 7, 9, 10, 12. With an even count there are two middle values (the 5th and 6th, both 7), and the median is halfway between them. With an odd count it is the single middle value. The mode is the value that appears most often, here 7 (three times). Data can have one mode, several, or none when every value appears equally often.
Which to use depends on the data. One extreme value moves the mean but barely touches the median: the mean of 1, 2, 3, 4 and 100 is 22, while the median is 3. That is why house prices and incomes are usually reported as medians. The mode is the only one of the three that works for categories, like the most common shoe size.
mean = Σx ÷ n · median = middle of the sorted values · mode = most frequent value
- The mean, median and mode are the three standard measures of the centre (location) of a data set; the median is preferred when the data are skewed or have outliers. Source: NIST/SEMATECH e-Handbook of Statistical Methods, measures of location.
- US grade 6 standards ask students to summarise data with a measure of centre (median or mean) and to relate the choice to the shape of the data (6.SP.B.5). Source: Common Core State Standards, Grade 6 Statistics and Probability.
How the three averages behave
Small data sets that show when the mean, median and mode agree and when they don’t.
| Data | Mean | Median | Mode |
|---|---|---|---|
| 2, 4, 6, 8, 10 | 6 | 6 | none |
| 1, 2, 3, 4, 100 | 22 | 3 | none |
| 3, 3, 3, 3 | 3 | 3 | 3 |
| 5, 1, 4, 2, 3, 6 | 3.5 | 3.5 | none |
| 1, 1, 2, 2, 3 | 1.8 | 2 | 1, 2 |
| 10, 20, 30, 40 | 25 | 25 | none |
| 0.5, 1.5, 1.5, 2.5 | 1.5 | 1.5 | 1.5 |
| −3, −1, 0, 1, 3 | 0 | 0 | none |
| 7, 7, 7, 8, 100 | 25.8 | 7 | 7 |
| 12, 15, 15, 18, 20, 21 | ≈ 16.8333 | 16.5 | 15 |
Frequently Asked Questions
What if there are two modes?
Then the data are bimodal and both values are modes: 1, 1, 2, 2, 3 has modes 1 and 2. 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, take the two middle values and average them. For 3, 7, 8, 10 the middle values are 7 and 8, so the median is 7.5, which need not be in the data.
Is the average the same as the mean?
Usually, yes: “average” in everyday use means the arithmetic mean. Statisticians use average more loosely for any measure of centre, which is why it helps to say mean or median.