Updated June 17, 2026
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The mean is the sum of all values divided by the count; the median is the middle value when data is sorted; the mode is the value that appears most often. Together they describe where a data set is centered.
How to find the mean
Add all values together, then divide by the number of values.
Example: 3, 7, 7, 8, 10 → sum = 35 → 35 / 5 = mean of 7.
The mean is sensitive to outliers. One very large or small value pulls it away from the center of the rest of the data, which is why median is often preferred for income or house prices.
How to find the median
Sort the values from smallest to largest. If there is an odd number of values, the median is the middle one. If even, it is the average of the two middle values.
| Data set | Sorted | Median |
|---|---|---|
| 5, 1, 9, 3, 7 | 1, 3, 5, 7, 9 | 5 (3rd of 5) |
| 4, 8, 2, 6 | 2, 4, 6, 8 | (4+6)/2 = 5 |
For the data set 13, 16, 12, 14, 19, 12, 14, 13, 14: sorted = 12, 12, 13, 13, 14, 14, 14, 16, 19. The 5th value is the median: 14.
How to find the mode
Count how many times each value appears. The value with the highest count is the mode. A data set can have no mode (all unique), one mode (unimodal), or more than one mode (bimodal or multimodal).
Example: 3, 7, 7, 8, 10 → 7 appears twice, all others once → mode = 7.
For the set 1 through 10 (each appearing once), there is no mode because no value repeats.
When to use each
Use the mean when data is roughly symmetric and there are no extreme outliers, for example test scores in a classroom. Use the median when the data is skewed or contains outliers, for example household income in a city. Use the mode for categorical data or when you want the most typical category, for example the most popular shoe size sold. You can use standard deviation alongside the mean to describe spread.
A quick tip: mean vs median as an outlier detector
When the mean and median are very different, that gap signals skewness or outliers. If mean > median, a few high values are pulling the average up (right skew). If mean < median, low outliers are dragging it down (left skew).
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