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Median Calculator
A median calculator finds the middle value of a list of numbers, and it also gives you the mean, the mode, the range, and the full summary — sum, minimum, maximum, and standard deviation — so you can compare every measure at a glance. Type in your numbers separated by commas or spaces, and it sorts them, picks out the middle, and shows the working — no sign-up, no spreadsheet needed.
Separate numbers with commas or spaces. Decimals and negative numbers are fine.
| Sorted list | |
| Count | |
| Mean (average) | |
| Mode | |
| Range (max − min) | |
| Sum | |
| Minimum | |
| Maximum | |
| Standard deviation |
How it works
The median is the value sitting in the middle of a sorted list. To find it, the calculator first sorts your numbers from smallest to largest. If there is an odd count, the median is the single number in the exact middle. If there is an even count, there is no single middle number, so the median is the average of the two middle numbers. Either way, half the values are below the median and half are above it.
Alongside the median, the calculator works out the mean and the mode, the other two common averages. The mean is the familiar average: add up every number and divide by how many there are. The mode is the number that appears most often; a list can have one mode, two modes, several modes, or no mode at all if every value appears exactly once. The three measures often disagree, and seeing them together tells you more about your data than any one of them alone.
Even count: median = (middle value 1 + middle value 2) ÷ 2
Mean = sum of all values ÷ count • Mode = most frequent value
The median is the honest average when your data has outliers. Imagine nine people in a room where eight earn around $50,000 and one earns $5,000,000: the mean salary would be over $600,000, which describes nobody in the room, while the median would be about $50,000 — the typical person. That is why house prices, salaries, and incomes are usually reported as medians. The mean is still the right choice when every value matters equally, such as averaging test scores or finding the average weight of packages for shipping.
Sorting is the step students most often skip, and it is the step that matters most: the median of an unsorted list is meaningless, because "middle" only makes sense once the numbers are in order. The calculator shows the sorted list in its results table so you can count to the middle yourself and check the answer. It also shows the range — the maximum minus the minimum — which gives a quick sense of how spread out the numbers are, plus the sum, the smallest and largest values, and the standard deviation, which measures the typical distance of the values from the mean (population standard deviation, dividing by the count of values).
Worked example
A teacher in Austin, Texas, collects seven quiz scores: 3, 1, 4, 1, 5, 9, 2. She wants the median, the mean, and the mode to understand how the class did.
Step 1 — sort the numbers: 1, 1, 2, 3, 4, 5, 9. Step 2 — find the middle: there are 7 values, so the middle is the 4th one, which is 3. That is the median. Step 3 — the mean: add them up, 3 + 1 + 4 + 1 + 5 + 9 + 2 = 25, then divide by 7 to get 25 ÷ 7 = 3.57. Step 4 — the mode: 1 appears twice and every other number appears once, so the mode is 1.
Notice how the three averages tell different stories: the median of 3 is the typical score, the mean of 3.57 is pulled up by the 9, and the mode of 1 shows the most common score. Enter the same list in the calculator above and you get the same result: median 3, mean 3.57, mode 1.
FAQ
What does the standard deviation tell you?
The standard deviation measures how spread out the numbers are around the mean. A small standard deviation means the values cluster close to the mean, while a large one means they are widely scattered. For the list 3, 1, 4, 1, 5, 9, 2 the mean is 3.57 and the standard deviation is about 2.61. This calculator uses the population standard deviation, which divides by the count of values.
What is the difference between the median and the mean?
The mean is the average: add all the numbers and divide by how many there are. The median is the middle value when the numbers are sorted. The mean uses every value, so one very large or very small number pulls it up or down, while the median only cares about the middle position and ignores extremes.
How do you find the median of an even number of values?
Sort the numbers, take the two middle values, and average them. For example, the sorted list 2, 4, 6, 8 has middle values 4 and 6, so the median is (4 + 6) / 2 = 5. With an odd count, the median is simply the single middle value.
What is the mode, and can there be more than one?
The mode is the value that appears most often in a list. Yes, there can be two modes (bimodal) if two values tie for the highest count, or more. If every value appears exactly once, the list has no mode at all.
When is the median better than the mean?
The median is better when the data is skewed by outliers. House prices are the classic example: a few very expensive homes drag the mean up, but the median still shows the price of a typical home. Income, salaries, and house prices are usually reported with medians for exactly this reason.