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Statistics · Descriptive Statistics Formula verified

Mean, Median, Mode Calculator

Type or paste a list of numbers to find the mean, median, mode, midrange, and quartiles, with a step-by-step breakdown of each one.

Numbers

Separate numbers with commas, spaces, or new lines.

Mean
18
6 numbers
Median
15.5
Mode
No mode
Midrange
23
Q1 · Q3 · IQR
8 · 23 · 15

Step-by-step proofCheck by hand

Mean, median, mode, midrange and quartiles

The mean adds every number and divides by the count. The median is the middle value once the list is sorted. The mode is whichever value repeats most often. Midrange averages just the smallest and largest value, ignoring everything in between. Quartiles go a step past the median: Q1 is the median of the lower half of the sorted list, and Q3 is the median of the upper half — together they, and the overall median, split the data into four equal-sized quarters.

The formulas

mean = Σx / n  ·  midrange = (min + max) / 2  ·  IQR = Q3 − Q1

Worked example

For 4, 8, 15, 16, 23, 42: mean = 18, median = 15.5, no value repeats so there's no mode, midrange = (4 + 42) / 2 = 23, and splitting the sorted list into halves gives Q1 = 8, Q3 = 23, so the interquartile range is 15.

Frequently asked questions

What are quartiles?
Quartiles split a sorted list into four equal-sized groups. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half — together with the overall median (which splits the data in half to begin with), they divide the list into quarters.
What does the interquartile range (IQR) tell you?
The IQR is Q3 minus Q1 — the spread of the middle 50% of the data, ignoring the smallest and largest quarters. It's a common way to describe how spread out typical values are without letting a few extreme outliers dominate the picture, the way the full range (max minus min) can.
What's the difference between midrange and median?
Midrange is just the smallest and largest value averaged together, so it's extremely sensitive to a single outlier — one unusually large number can drag it far from where most of the data actually sits. The median, being the middle value once everything is sorted, ignores exactly how far the extremes are and is much more resistant to outliers.
Sources and method
  • Standard descriptive statistics (mean, median, mode, midrange, and quartiles via the exclusive/Tukey method) — general published mathematics.
Last reviewed: 19 Sep 2026 Sources last verified: 19 Sep 2026 Results use the assumptions explained on this page. Report an error How we check calculations

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