Five-Number Summary

The five numbers

Every dataset can be summarized by five values:

1. Minimum — smallest value
2. Q1 — 25th percentile (first quartile)
3. Median (Q2) — 50th percentile (middle value)
4. Q3 — 75th percentile (third quartile)
5. Maximum — largest value

Step-by-step: {12, 15, 18, 22, 25, 28, 30, 35, 40}

$n = 9$ (already sorted).

• Min = 12
• Q1 = median of {12, 15, 18, 22} = $(15 + 18)/2 = 16.5$
• Median = 25 (5th value)
• Q3 = median of {28, 30, 35, 40} = $(30 + 35)/2 = 32.5$
• Max = 40

From summary to box plot

The five-number summary directly maps to a box plot: box from Q1 to Q3, line at median, whiskers to min and max (or to fences if checking for outliers).

Try it in the visualization

The data is sorted and each of the five values is marked. The box plot builds from these values. IQR and range are computed.