Statistics · Quick Reference

Box Plots Cheat Sheet

Statistics · Lesson 8/11

In one line: a box plot (or box-and-whisker plot) summarizes a dataset's distribution using five key numbers, making it easy to compare spread, center, and outliers at a glance.

Key Ideas

1Five-Number Summary. Minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum — the five values a box plot displays.

2Quartiles. Q1 is the median of the lower half of the data; Q3 is the median of the upper half. Together with the median, they divide the data into four equal parts.

3Interquartile Range (IQR). IQR = Q3 - Q1, representing the spread of the middle 50% of the data.

4The Box and Whiskers. The box spans from Q1 to Q3; a line inside marks the median. Whiskers extend to the minimum and maximum, excluding outliers.

5Identifying Outliers. A common rule: any value below Q1 - 1.5*IQR or above Q3 + 1.5*IQR is flagged as an outlier and plotted separately.

Worked Examples

Find the five-number summary of 2, 4, 6, 8, 10, 12, 14.

Min=2, Q1=4, Median=8, Q3=12, Max=14

Find the IQR for the dataset above.

IQR = 8

Using Q1=4 and Q3=12 (IQR=8), determine the outlier boundary values.

Any value below -8 or above 24 would be an outlier

Formulas

IQR = Q3 - Q1

Outlier bounds: below Q1 - 1.5*IQR or above Q3 + 1.5*IQR

Practice Yourself

What five values make up the five-number summary?

Minimum, Q1, median, Q3, maximum

Find the IQR if Q1=10 and Q3=25.

What does the 'box' in a box plot represent?

The middle 50% of the data, from Q1 to Q3