Five number summary calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- Sorted: 3, 5, 7, 8, 12, 13, 14, 18, 21.
- The median is the middle value (12). With an odd count it is left out when splitting into halves.
- Q1 is the median of the lower half and Q3 the median of the upper half; IQR = Q3 − Q1 = 10.
- Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as outliers.
| Inputs | Answer |
|---|---|
| Numbers: 3 7 8 5 12 14 21 13 18 | The five-number summary of 9 values is minimum 3, Q1 6, median 12, Q3 16, maximum 21. |
| Numbers: 1 2 3 4 5 6 7 8 | The five-number summary of 8 values is minimum 1, Q1 2.5, median 4.5, Q3 6.5, maximum 8. |
| Numbers: 10 12 12 13 14 15 16 40 | The five-number summary of 8 values is minimum 10, Q1 12, median 13.5, Q3 15.5, maximum 40. |
How to use it
The five-number summary lists the minimum, first quartile Q1, median, third quartile Q3 and maximum, the numbers behind a box plot. 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 middle value is left out of both halves.
The interquartile range IQR = Q3 − Q1 measures the spread of the middle half. A common rule flags values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as outliers. Different textbooks and software interpolate quartiles slightly differently, so small differences from other tools are normal.
Frequently asked questions
What is the five number summary?
Minimum, Q1, median, Q3 and maximum.
How do I find the quartiles?
Split the sorted data at the median and take the median of each half.
What counts as an outlier?
A value more than 1.5 × IQR below Q1 or above Q3 under the common rule.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.