Median Calculator
Find the median of a data set with the sorted list, its position, quartiles, interquartile range, five-number summary and outlier check, and see how it compares with the mean. Example: the median of 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56 is 23.
Show steps
How to use the Median Calculator
- Type or paste your numbers, separated by commas, spaces or new lines.
- Press Calculate to see the median, the sorted list, quartiles and any outliers.
Formula and method
Sort the data. If the count n is odd, the median is the value in position (n + 1) / 2. If n is even, the median is the average of the values in positions n / 2 and n / 2 + 1. The interquartile range is Q3 – Q1, and outliers fall below Q1 – 1.5 x IQR or above Q3 + 1.5 x IQR.
Worked example (odd count): 15 numbers
| Step | Result |
|---|---|
| Sorted | 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56 |
| Count | 15 (odd) |
| Position (15 + 1) / 2 | 8th value |
| Median | 23 |
Worked example (even count): 0, 1, 1, 18
| Step | Result |
|---|---|
| Count | 4 (even) |
| Middle values (2nd and 3rd) | 1 and 1 |
| Median (1 + 1) / 2 | 1 |
Median versus mean
| Data | Mean | Median | Better measure |
|---|---|---|---|
| 1, 2, 3, 4, 5 | 3 | 3 | Either |
| 1, 2, 3, 4, 100 | 22 | 3 | Median |
| Salaries with one executive | Higher | Lower | Median |
Why use the median
The median ignores how far extreme values are from the rest, so a single very large or small number does not move it. That is why reports on incomes and home prices use the median.
Frequently asked questions
How do I find the median?
Sort the numbers and take the middle one, or the average of the two middle ones if the count is even.
What is the median of 0, 1, 1, 18?
1.
What if there are two middle numbers?
Average them.
When should I use the median instead of the mean?
When the data is skewed or has outliers.
Does the median change with outliers?
Very little, which is its main advantage.
What is the median symbol?
Often x with a tilde, or M.
Sources
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