Histograms and box plots
Choose and read a display that summarises a numerical distribution.
Before you begin
- Counting frequencies
- Median and quartiles
Group numerical data into intervals
A histogram groups numerical values into intervals. For equal-width intervals, the bar height can show frequency. State boundary rules so every observation belongs to exactly one interval; for example, 0 ≤ x < 3 includes zero but excludes three. Adjacent intervals touch, unlike unrelated categories in a bar chart. Grouping helps reveal a pattern but hides the exact values inside each interval.
Show five summary values on a box plot
A simple box plot marks the minimum, Q1, median, Q3 and maximum on one numerical scale. The box extends from Q1 to Q3, and a line inside marks the median. Its width represents the IQR, not a count of observations. In this lesson the whiskers reach the minimum and maximum; some other conventions flag outliers separately, so check the key before interpreting a different plot.
Worked example
Place 0, 1, 1, 2, 3, 3, 4, 5, 7 and 8 into intervals [0,3), [3,6), [6,9).
Show the worked solution
- [0,3) contains 0,1,1,2: four observations.
- [3,6) contains 3,3,4,5: four observations; [6,9) contains 7,8: two.
- Draw touching bars of equal width with heights 4,4,2. The total frequency is ten.
Frequencies 4, 4 and 2.
Try it yourself
In a box plot, what does the box from Q1 to Q3 represent?
Common mistakes
- State histogram interval boundaries to avoid double-counting.
- A wider box means a wider middle spread, not necessarily more observations.
What can you explain now?
Describe a min-to-max box plot for 2, 4, 4, 6, 8, 10, 12, 14 using the median-of-halves convention.
Compare with the explanation
Whiskers at 2 and 14; box from 4 to 11; median line at 7.
The lower half has median 4, the full list median 7 and upper half median 11. The box width is 7 and the full range is 12.
After trying it yourself, choose your next review. This is your self-assessment.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗