Five Number Summary Calculator

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 exclusive method: with an odd number of data points, the median itself is left out of both halves. This is also called Tukey’s method, and it is what Moore and McCabe’s textbook and the TI-83 use.

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.

There is a second convention, the inclusive method, which keeps the median in both halves. On that same seven-point set it would give Q1 = the median of (a, b, c, d) and Q3 = the median of (d, e, f, g). Neither is wrong, but they disagree, so a quartile from one source will not always match a quartile from another. If your answer differs from a textbook by a small amount on an odd-sized dataset, this is almost always why.

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 such as income, house prices, and 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, since the calculator uses only the values you enter.