Box Plots
Box plots pack five numbers about a whole data set into one little picture — and the test loves to ask you to read them. Once you know what each line means, these become free points.
The five-number summary on a number line: min 52, Q1 60, median 68, Q3 74, max 90. The shaded box spans Q1 to Q3 (the middle 50%).
| Part | What it is | How to find it |
|---|---|---|
| Left whisker | Min to Q1 (bottom 25%) | Tip = minimum value |
| Box | Q1 to Q3 (middle 50%) | IQR = Q3 − Q1 |
| Inside line | Median (middle value) | Line inside the box |
| Right whisker | Q3 to Max (top 25%) | Tip = maximum value |
Each piece of a box plot and what it tells you.
When a question shows two box plots stacked, you usually compare medians (which set is centered higher?) or compare IQRs/ranges (which set is more spread out?). Read the axis carefully and line up each marker with its value.
That's the whole topic. Decode the five lines, remember IQR = Q3 − Q1, and know what a box plot can't tell you.
The ages of 7 children in a class are 6, 8, 8, 9, 10, 11, 12. What is the median age?
Worked examples
A box plot of daily high temperatures (in °F) shows: minimum = 52, Q1 = 60, median = 68, Q3 = 74, maximum = 90. What is the interquartile range (IQR) of the temperatures?
The box plot below summarizes the number of books read by students in a class. The median is 7, Q1 is 4, and Q3 is 11. Which of the following statements must be true?
Two box plots compare test scores for Class A and Class B. Class A: min 50, Q1 70, median 80, Q3 88, max 95. Class B: min 40, Q1 65, median 80, Q3 92, max 100. Both classes have the same median. Which class has the larger interquartile range, and by how much?
Common pitfalls
A box plot only shows the median, quartiles, min, and max. The mean is invisible — if an answer choice asserts a mean, it's almost always a trap.
Every section (whisker or box-half) holds about 25% of the data regardless of width. Width shows spread, not count — a long whisker just means those values are stretched out.
Range = max − min (uses the whisker tips). IQR = Q3 − Q1 (uses the box edges). Mixing them up gives a wrong but tempting number.
The line inside the box is the median, not the average and not the middle of the box. It can sit off-center, which actually tells you the data is skewed.
Key takeaways
A box plot displays five numbers: minimum, Q1, median, Q3, and maximum.
The box spans Q1 to Q3 and contains the middle 50% of the data; each of the four sections holds ~25%.
IQR = Q3 − Q1 (spread of the middle half); Range = Maximum − Minimum.
You cannot determine the mean or the exact number of data points from a box plot.
When comparing two box plots, check medians for center and IQR/range for spread separately.
Try it yourself
5 practice questions on Box Plots, drawn from the question bank. The tutor is one click away if you get stuck.