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Statistics — Quartiles
Median, Quartile & IQR Calculator
Paste your data to get the median, quartiles (Q1 and Q3), interquartile range, the five-number summary and any outliers.
Median
—
The middle value of your sorted data.
| Count n | — |
|---|---|
| Minimum | — |
| Q1 lower quartile | — |
| Q3 upper quartile | — |
| Maximum | — |
| IQR Q3 − Q1 | — |
| Outliers 1.5 × IQR rule | — |
Show our math
Enter your figures above to see the step-by-step working.
Paste comma, space or line-separated numbers — sorted for youEverything computed client-side — nothing leaves this page
How the Median & Quartile Calculator Works
The calculator sorts your data and reports the full five-number summary: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum. The median is the middle value; Q1 and Q3 are the medians of the lower and upper halves. The interquartile range (IQR) is Q3 minus Q1 — the spread of the middle half of the data.
It also flags outliers using the standard 1.5×IQR rule: any value more than 1.5 IQRs below Q1 or above Q3. Quartiles here use the “median of halves” method taught in most introductory statistics courses; other software may use slightly different interpolation.
IQR = Q3 − Q1 · outlier if x < Q1 − 1.5·IQR or x > Q3 + 1.5·IQR
Frequently Asked Questions
How is the median calculated?
Sort the numbers and take the middle one. If there is an even count, the median is the average of the two middle values. For 3, 7, 8, 12, 15, 19 the median is (8 + 12) / 2 = 10.
How are Q1 and Q3 found?
Split the sorted data at the median into a lower and an upper half. Q1 is the median of the lower half and Q3 is the median of the upper half. The middle value is excluded from both halves when the count is odd.
What counts as an outlier?
By the common 1.5×IQR rule, a value is an outlier if it falls more than 1.5 interquartile ranges below Q1 or above Q3. The calculator lists any such values.
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