Definition: The median is the middle value of a data set when the numbers are listed in order, or the mean of the two middle values when there is an even count.
What is the median?
The median splits an ordered data set in half, with as many values below as above.
How do you find it?
- Order the data from least to greatest.
- If the count is odd, take the middle value.
- If the count is even, average the two middle values.
For 17, 4, 22, 9, 13, ordering gives 4, 9, 13, 17, 22. The middle value is 13.
For 5, 8, 11, 20, 26, 31, the middle two are 11 and 20. Their mean is 31 / 2 = 15.5.
Why use it?
The median resists outliers. House prices are usually reported by median because a few mansions would inflate the mean.
What is the common error?
Forgetting to sort first. The middle of the unsorted list 17, 4, 22, 9, 13 would be 22, which is wrong. Sorting always comes first.
Example: The median of 3, 7, 7, 10, 40 is 7.