What Do You Do If There Is Two Medians? How to Handle It
If your data set has an even number of values, there isn’t one middle number — there are two — and the standard fix is to add those two middle values together and divide by two to get a single median. So the direct answer to “what do you do if there is two medians” is: average them. The result is your median, even if it’s a decimal that never appeared in the original list. For example, the two middle values 4 and 5 give a median of (4 + 5) / 2 = 4.5, which is a perfectly valid answer.
Why Two Middle Values Happen
The median is the value that splits an ordered data set into a lower half and an upper half Wikipedia. When you line up an even count of numbers, the split falls between two values instead of landing on one. That’s not a flaw in the method — it’s just what happens when there’s no center position to occupy.
Here’s the key misconception to clear up: the data set does not have two medians. It has two middle values, and those are different things. The two middle values are just the pair of numbers straddling the center point of your ordered list. The median is the single summary number you derive from them.
Think of it like a fence dividing a field in half. If you have an even number of fence posts, the dividing line falls between two posts rather than through one. The line still exists, and it’s still one line — you just have to decide where to place it, and the convention is to place it exactly halfway between the two posts.
Average the Middle Two
Arrange the values in ascending order. If the count is even, take the two values in the middle positions and compute their arithmetic mean. That single number is the median Statistics LibreTexts.
A quick way to find the middle positions without counting by hand: if n is the number of values, the two middle positions are n/2 and n/2 + 1. For n = 8, that’s position 4 and position 5. For n = 20, it’s position 10 and position 11.
Worked example
Take the ordered set: 2, 3, 5, 8, 11, 14, 15, 19.
That’s 8 values, so the middle positions are the 4th and 5th: 8 and 11. Average them: (8 + 11) / 2 = 9.5. The median is 9.5, even though 9.5 isn’t in the original list. That’s completely fine — the median doesn’t have to be one of your data points.
Median vs. Mean Confusion
A lot of the confusion around “two medians” actually comes from mixing up the median with the mean. The mean is the arithmetic average: add every value and divide by how many there are. The median is the positional middle. They answer different questions.
People sometimes see two clusters of numbers — two peaks — and assume the data has two medians. That description actually matches bimodal data, which has two modes (the most frequent values), not two medians. A data set always resolves to exactly one median under the standard convention.
Other times, someone eyeballs a spreadsheet, spots what looks like two central values, and isn’t sure which to report. The answer is both — you average them. You never simply pick one and discard the other.
Why does this distinction matter in practice? The median is resistant to extreme values in a way the mean is not Wikipedia. Consider incomes: 40, 45, 50, 55, 60. The mean is 50 and the median is 50. Now add a single huge outlier, say 1,000: the list becomes 40, 45, 50, 55, 60, 1000. The mean jumps to about 208, but the median becomes (50 + 55) / 2 = 52.5 — barely moved. That robustness is exactly why the median is preferred for skewed data, such as income or house prices.
Odd vs. Even Counts
The rule for finding the median depends entirely on whether your count is odd or even Khan Academy. Here’s the side-by-side:
| Number of values | Middle position(s) | How to get the median |
|---|---|---|
| Odd (e.g., 7) | One position: (n + 1) / 2 | Pick that single middle value |
| Even (e.g., 8) | Two positions: n/2 and n/2 + 1 | Average those two values |
With seven ordered values, the middle position is (7 + 1) / 2 = 4, so you take the 4th value directly. With eight values, there’s no single position to point to, so you average the values at positions 4 and 5.
For an odd count, the median is always one of the values already in your list. For an even count, it’s the average of the two middle values, which may or may not match one of them. If both middle values happen to be identical — say, 7 and 7 — the median is just 7. This means the “two medians” problem only ever appears with even-sized data sets.
Key Takeaways
- With an even number of values, there are two middle values, not two medians — average them to get the single median.
- The formula is simple: (middle value 1 + middle value 2) / 2.
- Find the middle positions with n/2 and n/2 + 1 for even counts, or (n + 1) / 2 for odd counts.
- The median can be a decimal that doesn’t appear in your data — that’s expected and correct.
- Don’t confuse the median with the mean, and don’t confuse two middle values with two modes in bimodal data.
- The median’s resistance to outliers makes it the better measure of center for skewed data like income or home prices.
