How to use the Median, Mode & Range
- Paste or type your numbers separated by commas, spaces or line breaks.
- Read the median — the middle value once the list is sorted, or the average of the two middle values when the count is even.
- Check the mode line: it lists every value tied for the highest frequency, and says 'no mode' when all values appear once.
- Compare the median against the mean to detect skew — a mean well above the median means a long right tail.
- Use Q1, Q3 and the interquartile range to spot outliers, which conventionally sit more than 1.5 × IQR beyond either quartile.
How the calculation works
The median is the order statistic at the middle position. Because it depends only on rank and not on magnitude, one absurd value cannot drag it around: replacing the largest number in a list with a billion changes the mean enormously and the median not at all. That robustness is why incomes, house prices and response times are reported as medians while temperatures and test scores are usually reported as means.
The mode is the most frequently occurring value, and it is the only summary that works on categorical data — you can find the modal colour of a car park but not its mean colour. A data set can be bimodal or multimodal, which is often the most interesting thing about it: two peaks usually mean two populations have been mixed together and should be analysed separately.
Quartiles are computed with linear interpolation between order statistics, the method used by R's default type-7 quantile and by most spreadsheet QUARTILE functions. Other conventions exist — some textbooks exclude the median when splitting the halves — and they can differ by a fraction of a unit on small samples. The difference never matters for interpretation and always matters if you are checking against a specific textbook answer.
Median = x₍ₙ₊₁₎/₂ for odd n, (x₍ₙ/₂₎ + x₍ₙ/₂₊₁₎)/2 for even n; Range = max − min; IQR = Q3 − Q1Source: Hyndman & Fan, 'Sample Quantiles in Statistical Packages', The American Statistician 50(4), 1996 — type 7 definition; Tukey, Exploratory Data Analysis (1977) for the 1.5 × IQR outlier fence.
Worked example
Eight support tickets took 7, 3, 9, 3, 12, 8, 3 and 15 minutes to resolve. Summarise them.
- Sort: 3, 3, 3, 7, 8, 9, 12, 15.
- n = 8 is even, so the median is the average of the 4th and 5th values: (7 + 8) ÷ 2 = 7.5 minutes.
- The value 3 appears three times and nothing else repeats, so the mode is 3.
- The mean is 60 ÷ 8 = 7.5 minutes, and the range is 15 − 3 = 12.
Median 7.5, mode 3, range 12. The mode reveals a cluster of very quick tickets that the mean alone hides completely.
Frequently asked questions
Can a data set have more than one mode?+
Yes. When several values tie for the highest frequency the set is bimodal or multimodal and the calculator lists all of them.
Median or mean — which should I report?+
Use the median when the data is skewed or contains outliers, such as salaries or waiting times. Use the mean for roughly symmetric data where every value should carry equal weight.
Why does my textbook give a different Q1?+
There are nine accepted quartile conventions. This calculator uses the interpolated type-7 method that R and most spreadsheets use.
Does the order I enter numbers in matter?+
No. The list is sorted internally before any order statistic is computed.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.