About the Five Number Summary Calculator
This five number summary calculator describes a data set with five values: the minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum. Paste or type your numbers in any order and it sorts them, finds the five numbers and adds the range, the interquartile range (IQR), the mean and the 1.5 × IQR outlier fences, with a sorted list so you can check the working.
The five number summary is the standard first look at a distribution in introductory statistics and AP Statistics, and it is exactly what a box-and-whisker plot draws. Teachers use it to summarise test scores, analysts use it for salaries, response times or prices, and anyone comparing two groups can line up their summaries side by side.
Quartiles are defined slightly differently by different textbooks and software, so choose the method you need: median of halves (TI-83/84 calculators and most courses), inclusive (Excel QUARTILE.INC, Google Sheets, NumPy) or exclusive (Excel QUARTILE.EXC). The minimum, median and maximum are the same under every method.
How to use the five number summary calculator
- 1Paste or type your numbers, separated by commas, spaces or new lines.
- 2Choose the quartile method your course or software uses.
- 3Read the five number summary at the top, then the individual values.
- 4Check the IQR and outlier list before drawing a box plot.
Formula and method
Sort the data from smallest to largest. The minimum and maximum are the first and last values, and the median is the middle value (or the average of the two middle values when n is even). With the median-of-halves method, Q1 is the median of the lower half and Q3 the median of the upper half, leaving the overall median out of both halves when n is odd.
The inclusive method instead places Q1 at position 1 + 0.25(n − 1) in the sorted list and Q3 at 1 + 0.75(n − 1), interpolating between neighbours; the exclusive method uses positions 0.25(n + 1) and 0.75(n + 1). Values beyond 1.5 IQRs from the quartiles are flagged as possible outliers (Tukey’s rule).
- Q1
- First quartile — 25% of values lie at or below it
- Q3
- Third quartile — 75% of values lie at or below it
- IQR
- Interquartile range, the spread of the middle half
- n
- Number of values
Worked examples
13 test scores (median of halves)
The median is the 7th sorted value, 75. The lower half 52–73 has median (64 + 68) ÷ 2 = 66 and the upper half 78–99 has median (85 + 88) ÷ 2 = 86.5, so the summary is 52, 66, 75, 86.5, 99.
Same scores with Excel QUARTILE.INC
The inclusive method puts Q1 at position 1 + 0.25 × 12 = 4 (the 4th value, 68) and Q3 at position 10 (85). The minimum, median and maximum do not change.
Delivery times in days, with an outlier
With 10 values the median is (5.5 + 6.1) ÷ 2 = 5.8. Q1 is the median of the first five (4.8) and Q3 of the last five (7.4). The upper fence is 7.4 + 1.5 × 2.6 = 11.3, so 15.2 days is an outlier.
Frequently asked questions
How do you find the five number summary?+
Sort the data, take the smallest value (minimum) and largest (maximum), find the median, then find the medians of the lower half (Q1) and upper half (Q3). For 11, 12, 14, 15, 16, 18, 20 it is 11, 12, 15, 18, 20.
Do you include the median when finding Q1 and Q3?+
With the median-of-halves method used by TI calculators and most textbooks, no — when n is odd the median is left out of both halves. Excel’s QUARTILE.INC effectively includes it, which is why its quartiles can differ.
Why does my calculator give a different Q1 than Excel?+
There are several accepted quartile definitions. TI-84 uses medians of halves, Excel QUARTILE.INC and Google Sheets interpolate at 1 + p(n − 1), and QUARTILE.EXC uses p(n + 1). Pick the matching method above to reproduce your software.
What is the five number summary used for?+
It summarises the centre (median), spread (IQR and range) and shape of a distribution with five numbers that are not distorted by outliers, and it is the basis of the box-and-whisker plot.
Is the five number summary affected by outliers?+
The median and quartiles are resistant to outliers, but the minimum and maximum are by definition the most extreme values. That is why box plots usually stop the whiskers at the fences and draw outliers separately.