Box Plots & Quartiles · Grades 6–9
Box Plot and Quartile Worksheets
Find the median, quartiles and IQR from a data list, read a box plot, and compare two data sets side by side, with the 1.5 × IQR outlier rule in Grade 9.
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What it is
A box plot shows a data set with five numbers: the minimum, the lower quartile (Q1), the median, the upper quartile (Q3) and the maximum. The box runs from Q1 to Q3 and holds the middle half of the data; the line inside it is the median.
Why it matters
A box plot squeezes a whole data set into five numbers, so two groups can be compared at a glance: which is higher overall, and which is more spread out.
How to do it
- Sort the data from least to greatest.
- The median is the middle value (or the mean of the middle two).
- Q1 is the median of the lower half; Q3 is the median of the upper half. With an odd count, leave the median out of both halves.
- Range = max − min. Interquartile range (IQR) = Q3 − Q1.
- Outlier test: a value above Q3 + 1.5 × IQR or below Q1 − 1.5 × IQR is an outlier.
Examples by level
Use the data list or the box plot to answer each question.
- BeginnerPoints scored in each game: 14, 16, 18, 19, 30, 31, 39, 40. Find the median.Answer24.5
- IntermediateMedian =Answer26
- AdvancedWhich is more spread out, by IQR (points per game)?AnswerTeam A
Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.
Common mistakes
- Finding the median of an unsorted list.
- Including the median in both halves when the count is odd.
- Reading the box's length as the range instead of the IQR.
Tips
- Each of the four sections of a box plot holds about a quarter of the data.
- A longer box means the middle of the data is more spread out.
For parents
Ask what the middle value is, then what the middle of each half is: that's the median and the two quartiles.
For teachers
Have students build a box plot from a short list before reading printed ones, so the five numbers mean something.
Key vocabulary
- quartile
- a value that splits sorted data into quarters
- interquartile range (IQR)
- Q3 − Q1, the spread of the middle half
- five-number summary
- minimum, Q1, median, Q3, maximum
Frequently asked questions
- How do you find the quartiles?
- Sort the data and find the median. Q1 is the median of the lower half and Q3 of the upper half; leave the median out of both halves when the count is odd.
- What does the box show?
- The middle half of the data, from Q1 to Q3. Its length is the interquartile range (IQR).
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