What is a five number summary?

The five number summary describes a data set using five key values: the minimum (smallest value), the first quartile Q1 (25th percentile), the median Q2 (50th percentile), the third quartile Q3 (75th percentile), and the maximum (largest value). Together they give a compact picture of the centre, spread, and range of the distribution.

What is a five number summary used for?

The five number summary is the foundation of the box-and-whisker plot, which is one of the most widely used charts for visualising data distributions. It quickly conveys where data are concentrated (the box from Q1 to Q3) and how far the tails extend. It also shows the range and makes it easy to spot asymmetry in the distribution.

How does the five number summary differ from the mean and SD?

The five number summary uses medians and quartiles, which are resistant to the influence of outliers. The mean and standard deviation can be heavily distorted by a single extreme value. For skewed data or data with outliers, the five number summary often gives a more informative picture of the typical value and spread.

Five Number Summary Calculator

The five number summary condenses the distribution of a data set into just five key values: the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum. Together these five numbers tell you where the data starts and ends, where the centre sits, how spread the middle half is (captured by the distance from Q1 to Q3, known as the interquartile range), and whether the distribution is symmetric or skewed. The five number summary is the direct input for a box-and-whisker plot (also called a box plot), which is one of the most efficient charts for comparing distributions side by side. The minimum and maximum are simply the smallest and largest values in the data set. Q1 and Q3 are the 25th and 75th percentiles, calculated using linear interpolation. The median is the 50th percentile. The IQR (Q3 minus Q1) represents the spread of the central 50% of the data. The full range is the maximum minus the minimum. This calculator accepts any comma-separated list of numbers and sorts them automatically before performing the calculations. At least four values are needed to produce meaningful quartiles. The results are useful for students writing statistics reports, teachers preparing class data, researchers summarising a data set before further analysis, and anyone comparing groups of data in a concise format. Because the five number summary relies on medians and quartiles rather than means, it is more resistant to the effect of outliers than summary statistics based on averages.

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Data values (comma-separated)

9.00

median (Q2)

Minimum3.00

Q15.00

Q313.00

Maximum15.00

IQR8.00

Range12.00

How it works

The calculator sorts the data in ascending order. Minimum is sorted[0] and maximum is sorted[n-1]. Quartiles are calculated by linear interpolation: rank position L = (p/100) x (n+1), and if L falls between positions the value is interpolated between the two neighbouring data points. IQR = Q3 minus Q1. Range = maximum minus minimum. A minimum of four values is required for all five numbers to be meaningful.

Worked example

Data: 3, 5, 7, 9, 11, 13, 15 (n = 7, already sorted). Minimum = 3. Q1 rank = 0.25 x 8 = 2.0, so Q1 = sorted[1] = 5. Median rank = 4.0, so median = sorted[3] = 9. Q3 rank = 6.0, so Q3 = sorted[5] = 13. Maximum = 15. IQR = 13 - 5 = 8. Range = 15 - 3 = 12. These match the default values pre-filled above.

Related calculators

Quartile and IQR Calculator: compute Q1, Q2, Q3, and IQR with Tukey fences.
Outlier Calculator: identify data points that fall outside the IQR fences.
Percentile Calculator: find any percentile rank, not just the standard quartiles.
Frequency Distribution Calculator: build a frequency table showing counts and percentages.

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