01 Key Concepts
Finding the Median (Odd Count)
Arrange values in order; the median is the single middle value.
Finding the Median (Even Count)
Arrange values in order; the median is the average of the two middle values.
Why the Median Resists Outliers
It only depends on the position of values, not their exact size, so one extreme value barely shifts it.
Median 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.
Median of Grouped Data
For large datasets organized into classes/intervals, the median can be estimated using cumulative frequency and interpolation.
02 Key Formulas
- Odd n: median = middle value after sorting
- Even n: median = average of the two middle values
03 Solved Examples
Example 1 Find the median of 3, 7, 9, 12, 20.
- The data is already sorted: 3, 7, 9, 12, 20.
- There are 5 values (odd count), so the median is the 3rd value.
Answer: 9
Example 2 Find the median of 4, 8, 15, 16, 23, 42.
- The data is sorted with 6 values (even count).
- The two middle values are 15 and 16.
- Average them: (15+16)/2.
Answer: 15.5
Example 3 Compare the mean and median of 10, 12, 14, 16, 500.
- Mean = (10+12+14+16+500)/5 = 552/5 = 110.4.
- Median: sorted data is 10,12,14,16,500; middle value is 14.
Answer: Mean = 110.4 (skewed by the outlier), Median = 14 (much more representative)
04 Practice Questions
1Find the median of 1, 3, 5, 7, 9.
5
2Find the median of 2, 4, 6, 8.
5
3Find the median of 10, 20, 30, 40, 50.
30
4Find the median of 6, 2, 9, 4.
5 (sorted: 2,4,6,9; average of 4 and 6)
5Why is the median often better than the mean for income data?
Income tends to be skewed by a few very high earners, and the median resists that skew
📄 Median — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.