Statistics · Quick Reference

Median Cheat Sheet

Statistics · Lesson 3/11

In one line: the median is the middle value of an ordered dataset — a measure of central tendency that resists the pull of extreme outliers far better than the mean.

Key Ideas

1Finding the Median (Odd Count). Arrange values in order; the median is the single middle value.

2Finding the Median (Even Count). Arrange values in order; the median is the average of the two middle values.

3Why the Median Resists Outliers. It only depends on the position of values, not their exact size, so one extreme value barely shifts it.

4Median vs. Mean. For skewed data (like income, where a few very high earners exist), the median usually gives a more representative 'typical' value than the mean.

5Median of Grouped Data. For large datasets organized into classes/intervals, the median can be estimated using cumulative frequency and interpolation.

Worked Examples

Find the median of 3, 7, 9, 12, 20.

Find the median of 4, 8, 15, 16, 23, 42.

15.5

Compare the mean and median of 10, 12, 14, 16, 500.

Mean = 110.4 (skewed by the outlier), Median = 14 (much more representative)

Formulas

Odd n: median = middle value after sorting

Even n: median = average of the two middle values

Practice Yourself

Find the median of 1, 3, 5, 7, 9.

Find the median of 2, 4, 6, 8.

Find the median of 10, 20, 30, 40, 50.