Mean, Median & Mode Calculator
Mean, median, mode and range of a list of numbers in one go.
Quick answer
- The mean uses every value, the median is the middle value, and the mode is the most frequent — comparing them exposes skewed data at a glance.
- Quartiles here use Tukey's median-of-halves method: Q1 and Q3 are the medians of the lower and upper halves, and the IQR (Q3 − Q1) covers the middle 50% of the data.
- Values outside the Tukey fences [Q1 − 1.5 × IQR, Q3 + 1.5 × IQR] are listed as outliers — check them before trusting the mean.
- Worked example — Mean: 2.40 (full example below).
Mean, Median & Mode Calculator
| Mean | 2.40 |
| Median | 2.00 |
| Mode | 2 |
| Range | 3.00 |
| First quartile (Q1) | 1.50 |
| Third quartile (Q3) | 3.50 |
| Interquartile range (IQR) | 2.00 |
| Outliers (Tukey fences) | None |
| Frequency table | 1 ×1 · 2 ×2 · 3 ×1 · 4 ×1 |
For 1, 2, 2, 3, 4: the mean is 12 ÷ 5 = 2.4, the median (middle value) is 2, the mode is 2 because it appears twice, and the range is 4 − 1 = 3.
Mean, median and mode are three different kinds of 'average', and each tells you something different about a data set. The mean uses every value, the median is the middle value, and the mode is the value that occurs most often.
Enter a comma-separated list to get all three plus the range (highest minus lowest). Comparing the mean and median is a quick way to spot skewed data — if they differ a lot, a few extreme values are pulling the mean around.
The formula
Worked example
For 1, 2, 2, 3, 4: the mean is 12 ÷ 5 = 2.4, the median (middle value) is 2, the mode is 2 because it appears twice, and the range is 4 − 1 = 3.
The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.
When this estimate may be wrong
- When the mean misleads: in 1, 2, 2, 3, 4, 100 the single outlier 100 drags the mean up to 18.67, even though five of the six values are 4 or less. The median (2.5) describes the typical value far better — the Tukey fences for this set are −1 and 7, which is why 100 is flagged as an outlier.
- Quartile values depend on the convention used: this calculator uses Tukey's median-of-halves method, and other methods (inclusive percentiles, linear interpolation) can give slightly different Q1 and Q3 on small data sets.
Frequently asked questions
What if no value repeats?
Then the data set has no mode, and the calculator says so. That is normal for measurements like heights, where every value may be unique.
What if two values tie for most frequent?
The data is called bimodal and both values are listed as the mode. With even more ties, all of them are shown.
Which average should I use?
Use the median when the data has outliers — house prices are the classic example. Use the mean when every value should count equally, and the mode for the most typical category or size.
How are Q1, Q3 and the outliers calculated here?
By Tukey's median-of-halves method: Q1 is the median of the lower half of the sorted data and Q3 the median of the upper half (with an odd count, the overall median belongs to neither half). The IQR is Q3 − Q1, and any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged as an outlier. Other quartile conventions exist and can give slightly different values on small data sets.
Category: Math calculators
Sources & methodology
Quartiles are computed with Tukey's median-of-halves (hinge) method: after sorting, Q1 is the median of the lower half and Q3 the median of the upper half, with the overall median excluded from both halves when the count is odd. Outliers are values outside [Q1 − 1.5 × IQR, Q3 + 1.5 × IQR]. The frequency table lists each distinct value once, in ascending order, with its count.
Content last reviewed by CalcHub Editorial.
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