Five Number Summary Calculator

A five number summary is a concise statistical description of a dataset using five key values: the Minimum, First Quartile (Q1), Median (Q2), Third Quartile (Q3), and Maximum. Together they capture the spread, center, and shape of a distribution and form the basis of a box-and-whisker plot.

First, sort all values in ascending order. Identify the minimum and maximum. Find the median (middle value, or average of two middle values for even-sized datasets). Then split the dataset into a lower half and upper half — the median of the lower half is Q1, and the median of the upper half is Q3. The method for splitting (inclusive vs. exclusive of the overall median) varies by convention.

The exclusive (Tukey) method excludes the overall median from both the lower and upper halves when the dataset has an odd number of values. The inclusive method includes the median in both halves. This can lead to slightly different Q1 and Q3 values. The exclusive method is most commonly taught in statistics courses and is the default here.

The IQR is Q3 minus Q1 and represents the middle 50% of the data. It is a robust measure of spread that is not affected by extreme values or outliers, making it more reliable than the full range for many datasets.

Outliers are commonly identified using Tukey's fences: any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is considered a potential outlier. This calculator highlights those values automatically after computing the summary.

You can separate your numbers with commas, spaces, semicolons, or line breaks — the calculator accepts all common formats. For example: 3, 7, 8, 5, 12 or 3 7 8 5 12 both work fine. Negative numbers and decimals are fully supported.

It gives a quick snapshot of your data's distribution without requiring detailed knowledge of all values. It reveals skewness (by comparing distances between the five numbers), the typical central value, and the spread. It is also the foundation for box plots, which visually compare distributions across groups.

This calculator works with raw individual data values. If you have grouped data or a frequency table, you would need to expand the frequencies into individual values before entering them — for example, entering a value of 5 that appears 3 times as: 5, 5, 5.