Find the mean, median, mode, and range of any list of numbers — paste your data in and get every summary statistic at once.
Mean is the sum of all values divided by the count. Median is the middle value once the list is sorted. Mode is the most frequently occurring value. Range is the highest value minus the lowest.
These three measures of "central tendency" can tell very different stories about the same data set, especially when outliers are present.
Example: for 4, 8, 6, 5, 3, 8, 9 — mean ≈ 6.14, median = 6, mode = 8, range = 6 (from 3 to 9).
| Data set | Mean | Median |
|---|---|---|
| 1, 2, 3, 4, 5 | 3 | 3 |
| 1, 2, 3, 4, 100 | 22 | 3 |
| 10, 20, 30, 40 | 25 | 25 |
How do you calculate the average (mean)? Add all the numbers together, then divide by how many numbers there are. The average of 4, 8, and 6 is (4+8+6)/3 = 6.
How do you find the median? Sort the numbers from smallest to largest. If there's an odd count, the median is the middle value; if even, it's the average of the two middle values.
What is the mode? The mode is the value (or values) that appear most often in a data set. A set can have one mode, multiple modes, or no mode if every value is unique.
When should you use median instead of average? Median is more useful than average when a data set has extreme outliers, since a few very high or very low values can skew the average but not the median.
What is the range of a data set? Range is the difference between the largest and smallest values in a data set, giving a quick sense of how spread out the data is.
Example 1 — Test scores: 85, 90, 78, 92, 88 → mean = 86.6, median = 88, range = 14.
Example 2 — Odd number of values: 4, 8, 6, 5, 3, 8, 9 → sorted: 3,4,5,6,8,8,9 → median = 6, mode = 8.
Example 3 — With an outlier: 1, 2, 3, 4, 100 → mean = 22, median = 3 — the median better reflects the "typical" value here.
Five salaries in thousands are 40, 45, 50, 52 and 300. The mean is (40 + 45 + 50 + 52 + 300) ÷ 5 = 97.4, which is higher than four of the five values because one large salary pulls it up. The median is 50, which describes the typical person much better. When data contains outliers, the median is the safer summary.
| Question | Use |
|---|---|
| What is the overall level, including every value? | Mean |
| What does a typical value look like? | Median |
| Which value occurs most often? | Mode |
| How spread out is the data? | Range |
What if there are two middle numbers? When the list has an even number of values, the median is the average of the two middle numbers.
Can a data set have more than one mode or none? Yes. If several values tie for most frequent, each is a mode, and if every value appears once there is no mode.