Mode, Median and Mean Calculator
Find the mean, median, mode and range of any data set instantly. Paste your numbers and this calculator returns all three averages plus a step-by-step breakdown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the steps
How the Mode, Median and Mean Calculator Works
Paste or type a list of numbers and this calculator instantly reports the three measures of central tendency — the mean, the median and the mode — plus the range. Numbers can be separated by commas, spaces or new lines, so you can drop in a column copied from a spreadsheet.
The Formulas
Mean = sum of all values ÷ count Median = the middle value of the sorted list (or the average of the two middle values for an even count) Mode = the value (or values) that appear most often
The range, a simple measure of spread, is the maximum value minus the minimum.
Worked Example
Take the data set 4, 8, 15, 16, 23, 42, 8:
- Mean = (4 + 8 + 15 + 16 + 23 + 42 + 8) ÷ 7 = 116 ÷ 7 ≈ 16.57
- Sorted: 4, 8, 8, 15, 16, 23, 42 → Median = the 4th value = 15
- Mode = 8 (it appears twice, more than any other value)
- Range = 42 − 4 = 38
When the Three Averages Disagree
| Data set | Mean | Median | Mode |
|---|---|---|---|
| 5, 5, 5, 5 | 5 | 5 | 5 |
| 1, 2, 3, 4, 5 | 3 | 3 | none |
| 2, 2, 2, 50 | 14 | 2 | 2 |
The third row shows why the choice matters: the single large value (50) drags the mean up to 14, while the median and mode both stay at 2, the typical value.
Choosing the Right Measure
Use the mean for symmetric data with no extreme outliers, the median for skewed data such as incomes or prices, and the mode for categorical or repeated values where you care about the most common result. Reporting all three together gives the fullest picture of your data.
Frequently asked questions
What is the difference between mean, median and mode?+
The mean is the arithmetic average — add all values and divide by how many there are. The median is the middle value once the numbers are sorted. The mode is the value that appears most often. They are three different ways to describe the center of a data set, and they can give very different answers when data is skewed.
How do you find the median of an even set of numbers?+
Sort the numbers, then take the two middle values and average them. For the set 2, 4, 6, 8 the two middle values are 4 and 6, so the median is (4 + 6) ÷ 2 = 5. With an odd count, the median is simply the single middle value.
Can a data set have more than one mode?+
Yes. A set with two values tied for most frequent is bimodal, and one with several ties is multimodal. If every value appears the same number of times, statisticians usually say there is no mode. This calculator lists every value that ties for the highest frequency.
When should I use the median instead of the mean?+
Use the median when your data has outliers or a skewed distribution, such as house prices or incomes. A few very large values pull the mean upward, but the median stays near the typical value, giving a more representative center.
What is the range and how is it calculated?+
The range measures spread: it is the largest value minus the smallest value. For the set 4, 8, 15, 42 the range is 42 − 4 = 38. A larger range means the data is more spread out, though it only reflects the two extremes, not the values in between.