Five Number Summary Calculator
Calculate five number summary (min, Q1, median, Q3, max) and IQR from up to 10 data values.
Enter values in any order — the calculator sorts them.
The five number summary describes a dataset with five key values: minimum, Q1 (first quartile), median (Q2), Q3 (third quartile), and maximum. These five numbers are what a box plot displays visually.
Quartile calculation
Sort the data from smallest to largest. The median splits the dataset in half. Q1 is the median of the lower half, Q3 is the median of the upper half. The calculator uses the inclusive method: for an odd number of data points, the median itself is excluded from both halves.
With 7 data points (a, b, c, d, e, f, g): median = d, lower half = (a, b, c), Q1 = b, upper half = (e, f, g), Q3 = f.
IQR (Interquartile Range) = Q3 - Q1.
Outlier detection
The standard fence rule: a value is a suspected outlier if it falls below Q1 - 1.5×IQR or above Q3 + 1.5×IQR. Values beyond Q1 - 3×IQR or Q3 + 3×IQR are extreme outliers.
For example, with Q1 = 10, Q3 = 20, IQR = 10: lower fence = 10 - 15 = -5, upper fence = 20 + 15 = 35. Any data point below -5 or above 35 would be flagged.
Why it matters
The five number summary is robust to outliers in a way that the mean and standard deviation are not. A single extreme value shifts the mean significantly but barely changes the quartiles. This makes it the preferred summary for skewed distributions — income, house prices, medical costs.
The median of income data tells you more about typical experience than the mean, which gets pulled upward by billionaires.
Enter up to 10 values. Leave extra fields blank — the calculator uses only the values you enter.