Median Formula
Find the median of a data set.
The median is the middle value when data is sorted.
Learn how to handle both odd and even data sets.
The Formula
Odd count: Median = value at position (n + 1) / 2
Even count: Median = average of values at positions n/2 and (n/2 + 1)
Even count: Median = average of values at positions n/2 and (n/2 + 1)
The median is the middle value in a sorted data set. Unlike the mean, the median is not affected by extreme outliers.
Variables
| Symbol | Meaning |
|---|---|
| n | The total number of data values |
| (n + 1) / 2 | Position of the median when n is odd |
| n/2 and n/2 + 1 | Positions of the two middle values when n is even |
Example 1 — Odd Number of Values
Find the median of: 7, 3, 12, 5, 9
Step 1: Sort the data — 3, 5, 7, 9, 12
Step 2: n = 5 (odd), so median position = (5 + 1) / 2 = 3rd value
Median = 7 — The third value in the sorted list.
Example 2 — Even Number of Values
Find the median of: 4, 8, 15, 22, 30, 42
Step 1: Data is already sorted — 4, 8, 15, 22, 30, 42
Step 2: n = 6 (even), so take the 3rd and 4th values
Step 3: Median = (15 + 22) / 2
Median = 18.5 — The average of the two middle values.
When to Use It
Use the median when:
- Your data has outliers that would distort the mean (e.g., income data)
- You want to find the "typical" value in a skewed distribution
- Reporting real estate prices, salaries, or other data with extreme highs or lows
- You need a more robust measure of central tendency