Box Plots

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find the 5-number summary: 2, 4, 5, 7, 8, 10, 12, 14, 15.

Already sorted; 9 values. Median = 8. Lower half: 2, 4, 5, 7 ⇒ Q₁ = (4+5)/2 = 4.5. Upper half: 10, 12, 14, 15 ⇒ Q₃ = (12+14)/2 = 13. Min = 2, Max = 15.

Answer: Min=2, Q₁=4.5, Med=8, Q₃=13, Max=15

Worked example 2

For the data above, find the IQR.

Use the middle 50% spread: IQR = Q₃ - Q₁ = 13 - 4.5 = 8.5.

Answer: 8.5

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

Median of 1, 3, 5, 7, 9
Check
5
Min of 12, 4, 8, 15, 6
Check
4
Max of 22, 18, 25, 30, 19
Check
30
Q₁ of 2, 4, 6, 8, 10, 12
Check
4
Q₃ of 2, 4, 6, 8, 10, 12
Check
10
IQR of 3, 5, 7, 9, 11, 13, 15
Check
8
Range of 4, 10, 16, 22, 28
Check
24
Median of 5, 8, 11, 14, 17, 20
Check
12.5

Try this situation 1

Heights (in): 58, 60, 62, 63, 65, 67, 68, 70, 72. Find the 5-number summary.

Show a worked solution

Answer: Min=58, Q₁=61, Med=65, Q₃=69, Max=72.

Median is the 5th value = 65. Q₁ = (60+62)/2 = 61. Q₃ = (68+70)/2 = 69.

Try this situation 2

From the same data, find the IQR.

Show a worked solution

Answer: 8 in.

Use the middle 50% spread: IQR = 69 - 61 = 8.

Fresh questions · saved on this device

Practice this skill

12 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. Compare the five-number summaries. Class A: Min = 60, Q1 = 70, Median = 80, Q3 = 85, Max = 95. Class B: Min = 65, Q1 = 72, Median = 78, Q3 = 88, Max = 92. Which statement compares the interquartile ranges correctly?

Class A’s IQR is 15; Class B’s is 16. Class A’s IQR is 16; Class B’s is 15. Both IQRs are 15. The IQR uses the minimum and maximum, so Class A’s is 35 and Class B’s is 27.

2. The five-number summary for test scores is: Min = 55, Q1 = 65, Median = 75, Q3 = 85, Max = 100. If you move from Q1 to the median, how much do the scores increase?

5 points 10 points 15 points 20 points

3. The following data set represents the number of hours students studied for an exam: 2, 3, 4, 5, 5, 6, 7, 8, 9, 10. When displayed as a box plot, what value represents the median?

5 5.5 6 6.5

4. Two classes took a standardized test. The box plots below represent their scores. Class A: Minimum = 68, Q1 = 76, Median = 82, Q3 = 88, Maximum = 96 Class B: Minimum = 72, Q1 = 79, Median = 83, Q3 = 87, Maximum = 95 Which statement is true?

Class A has a larger range. Class B has a larger IQR. Both classes have the same median. Class A has a higher median than Class B.

5. A box plot displays the ages of volunteers at a community center. The whiskers extend from age 18 to age 65, and the box spans from Q1 = 28 to Q3 = 52. What is the range of the data?

24 years 28 years 47 years 52 years

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Statistics & Data quiz ↗Try a full practice test ↗

Summarize data with a box plot