Five-Number Summary Calculator
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The five-number summary describes a data set with five values: the minimum, the first quartile Q1, the median, the third quartile Q3 and the maximum. For 3, 5, 7, 8, 12, 13, 14, 18, 21, 40 it is 3, 7, 12.5, 18, 40, and 40 is an outlier.
Box plot: whiskers reach the most extreme values inside the fences; red circles are outliers.
| Five-number summary | |
| Minimum | 3 |
| First quartile Q₁ | 7 |
| Median | 12.5 |
| Third quartile Q₃ | 18 |
| Maximum | 40 |
| Spread | |
| Range (max − min) | 37 |
| Interquartile range (IQR) | 11 |
| Outlier fences | −9.5 to 34.5 |
| Outliers | 40 |
| Mean (for comparison) | 14.1 |
| Count n | 10 |
Show steps
- Sort the 10 values: 3, 5, 7, 8, 12, 13, 14, 18, 21, 40.
- Minimum = 3, maximum = 40.
- Median: the mean of positions 5 and 6: (12 + 13) ÷ 2 = 12.5.
- n is even, so split into two halves of 5. Q₁ is the median of the lower half (7), Q₃ the median of the upper half (18).
- IQR = Q₃ − Q₁ = 18 − 7 = 11. Outlier fences: 7 − 1.5 × 11 = −9.5 and 18 + 1.5 × 11 = 34.5.
- Outliers (outside the fences): 40.
How to use the five-number summary calculator
- Paste or type your numbers in any order.
- Choose the quartile method your class or software uses (the default matches most textbooks and the TI-84).
- Press Summarize to get the five numbers, the IQR, outliers and a box plot.
How to find the five-number summary by hand
- Sort the data from smallest to largest.
- The smallest value is the minimum; the largest is the maximum.
- The median is the middle value (or the mean of the two middle values).
- Q1 is the median of the lower half, Q3 the median of the upper half. With an odd count, leave the median out of both halves.
Example: 2, 4, 4, 5, 7, 9, 10. Median 5; lower half 2, 4, 4 gives Q1 = 4; upper half 7, 9, 10 gives Q3 = 9. Summary: 2, 4, 5, 9, 10.
Outliers and the 1.5 × IQR rule
The interquartile range IQR = Q3 − Q1 measures the spread of the middle half. A value is usually called an outlier if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. In the example at the top, IQR = 18 − 7 = 11, the upper fence is 18 + 16.5 = 34.5, so 40 is an outlier.
Why calculators give different quartiles
There is no single agreed rule for quartiles. The median-of-halves method, Excel’s QUARTILE.INC and QUARTILE.EXC can give slightly different Q1 and Q3 for the same data. The minimum, median and maximum never change. Use the method your teacher or software expects.
Five-number summary practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
What is the five-number summary?
Minimum, first quartile (Q1), median, third quartile (Q3) and maximum. Together they show the center, spread and range of a data set.
How is it related to a box plot?
A box plot is a picture of the five-number summary: the box runs from Q1 to Q3 with a line at the median, and whiskers reach toward the minimum and maximum.
Do I include the median when finding Q1 and Q3?
In the most common textbook method, no: with an odd number of values, leave the median out of both halves. Excel's QUARTILE.INC uses a different interpolation rule.
Does the five-number summary work for skewed data?
Yes. It is resistant to outliers, which makes it better than the mean and standard deviation for skewed data.
How many numbers do I need?
At least 3; the summary is more meaningful with more data.
Sources
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