Math calculator
Mean, Median & Mode Calculator
Summarize a list of numbers with the most common measures of center and spread.
Separate numbers with commas, spaces, or new lines.
Mean
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Eight numbers from one dataset
Paste a list separated by commas, spaces, or new lines, and the calculator sorts it internally to produce eight figures at once: mean, median, mode, range, minimum, maximum, count, and sum, plus the sorted list itself so you can see the order it worked from.
Take the dataset 7, 3, 7, 9, 5, 7, 2. Sorted, that's 2, 3, 5, 7, 7, 7, 9. The mean is 40 ÷ 7 ≈ 5.7143. The median — the middle value once sorted — is the 4th of 7 values, which is 7. The mode is also 7, since it appears three times while every other value appears once. The range is the highest value minus the lowest: 9 − 2 = 7.
Mode is the only one of the three that can come back empty: if every value in the list occurs the same number of times, the calculator reports "No mode" instead of picking one arbitrarily.
How the median handles even-sized lists
For an odd number of values, the median is simply the middle one after sorting, as in the 7-value example above. For an even number of values, there's no single middle entry, so the calculator averages the two values that sit in the middle. For 4, 8, 15, 16, the two middle values are 8 and 15, so the median is (8 + 15) ÷ 2 = 11.5.
The mean for that same four-value set is (4 + 8 + 15 + 16) ÷ 4 = 43 ÷ 4 = 10.75 — close to the median here because the values are fairly evenly spread, which won't hold once a dataset has a distant outlier.
Why mean and median can disagree — and when there's more than one mode
The mean factors in every value's exact distance from the others, so one extreme number pulls it hard in that direction. The median only cares about position in the sorted order, so it barely moves. Take 2, 3, 5, 7, 7, 7, 90 — swap the earlier example's 9 for 90 and the mean jumps to 121 ÷ 7 ≈ 17.2857, while the median stays at 7, because 90 is still just the largest of seven sorted values and doesn't change which one sits in the middle.
A dataset can also have more than one mode. For 1, 1, 2, 2, 3, both 1 and 2 appear twice — more than any other value — so the calculator lists both as modes rather than choosing one. This is sometimes called a bimodal dataset.
Reading these statistics day to day
Each of the three center measures answers a slightly different question, which is why real-world reporting often picks one over the others:
- Household budgeting – the median of four monthly grocery bills resists being skewed by one unusually expensive holiday month, unlike the mean
- Real estate listings – median home price is reported instead of mean because a few multimillion-dollar sales would otherwise distort a neighborhood's typical price
- Retail inventory – the mode of shoe sizes sold tells a store which size to stock the most of, something an average size in between whole sizes can't do
- Sports statistics – a basketball player's mean points per game summarizes season performance across every outing
- Customer ratings – the mode of a 1–5 star rating list shows the single most common reaction, separate from the mean star rating
- Classroom assessment – comparing the mean and median of test scores flags whether a few very low or very high scores are skewing the class average
Frequently asked questions
What's the actual difference between mean, median, and mode?
Mean adds every value and divides by the count. Median is the middle value once everything is sorted. Mode is whichever value repeats most often. For 2, 3, 5, 7, 7, 7, 9, that's a mean of about 5.7143, a median of 7, and a mode of 7.
Why does my dataset show "No mode"?
That happens when no value repeats more than any other — including when every value is unique. For 4, 8, 15, 16, 23, 42, each number appears exactly once, so there's no most-frequent value to report.
Can a dataset have more than one mode?
Yes. For 1, 1, 2, 2, 3, both 1 and 2 appear twice, tied for the highest frequency, so the calculator lists both. A dataset with two modes is called bimodal.
How is the median found when there's an even number of values?
It's the average of the two values sitting in the middle after sorting. For 4, 8, 15, 16, the middle pair is 8 and 15, so the median is (8 + 15) ÷ 2 = 11.5.
Why is the mean so different from the median in my results?
One or more extreme values are pulling the mean away from where most of the data sits, while the median mostly ignores how extreme a value is. Changing the top value of 2, 3, 5, 7, 7, 7, 9 to 90 lifts the mean from about 5.71 to about 17.29, but the median stays exactly at 7.
What does the range figure actually tell me?
Range is the maximum minus the minimum — a single number describing the total spread from lowest to highest. It ignores everything in between, so two datasets with the same range can still look very different once you check the mean, median, and mode.