Mean, Median, Mode Calculator
Paste a dataset to get the mean, median, mode, range, and quartiles — with the steps shown.
Quartiles use the median method: the median splits the data, then Q1 and Q3 are the medians of the lower and upper halves (the overall median is excluded from both halves when n is odd).
The mean is the sum divided by the count, the median is the middle value of the sorted data, and the mode is the value that appears most often. For 4, 8, 15, 16, 23, 42 the mean is 108 ÷ 6 = 18 and the median is (15 + 16) ÷ 2 = 15.5; that set has no mode because every value appears once.
Three ways to describe the “average”
“Average” is ambiguous — there are three common measures of central tendency, and they answer different questions. The mean balances the data: add every value and divide by how many there are. The median is the positional middle once the values are sorted, so half the data sits below it and half above. The mode is simply the most frequent value. When a dataset is symmetric the three land close together; when it’s skewed or has outliers they pull apart, and the gap between them tells you something about the shape of the data.
sum of all values divided by the count
Worked example
Six values: 4, 8, 15, 16, 23, 42.
- 1 Add the values for the mean. 4 + 8 + 15 + 16 + 23 + 42 = 108, then 108 ÷ 6 = 18.
- 2 Sort, then take the middle for the median. Already sorted; with 6 values the two middle ones are 15 and 16, so the median is (15 + 16) ÷ 2 = 15.5.
- 3 Count frequencies for the mode. Every value appears exactly once, so this dataset has no mode. If a value repeated most often, that value would be the mode.
Mean vs. median vs. mode
What each measures and when to reach for it.
| Measure | What it is | Best when |
|---|---|---|
| Mean | Sum ÷ count | Data is roughly symmetric with no extreme outliers |
| Median | Middle of the sorted values | Data is skewed or has outliers (e.g. income, prices) |
| Mode | Most frequent value | Categorical data, or when you want the most common value |
Reading the result
The median resists outliers. One extreme value drags the mean toward it but barely moves the median, because the median only cares about position. That’s why house prices and incomes are usually reported as medians — a few very large values would inflate the mean and misrepresent the “typical” case.
The mode works where the others don’t. The mode is the only one of the three that applies to categorical data (favourite colour, most-sold size), and a dataset can be multimodal — two or more values tying for most frequent — or have no mode at all when nothing repeats.
Quartiles and the IQR describe the spread. Q1 and Q3 mark the 25th and 75th percentiles, and the interquartile range (IQR = Q3 − Q1) is the width of the middle half of the data — a measure of spread that, like the median, ignores outliers. To quantify spread around the mean instead, use the standard deviation.