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.
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.