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Box plots Quiz

Grade 6 • 6M • 10 Questions (36 Marks)

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Box plots — Notes & Worked Examples Show / Hide

Explanation:

A box plot displays 5 key values: Minimum (left whisker), Lower Quartile (LQ) (left of box), Median (line inside box), Upper Quartile (UQ) (right of box), and Maximum (right whisker). The box width is the IQR = UQ − LQ (middle 50% of data).

When asked to compare two box plots (2 marks), always make two comparisons in context: (1) compare the medians (which group is higher on average), and (2) compare the IQRs or ranges (which group is more consistent / less spread out).

Example 1: A dataset has Minimum = 12, LQ = 20, Median = 28, Range = 35, and IQR = 16. Find the Maximum and UQ to plot the box plot.

12 20 28 36 47 10 20 30 40 50

Solution:

Max = 12 + 35 = 47; UQ = 20 + 16 = 36
Answer: UQ = 36, Maximum = 47

Example 2: Class A scores: Median = 64%, IQR = 14%. Class B scores: Median = 58%, IQR = 22%. Compare the two classes.

A B 30% 50% 70% 90%

Solution:

1. Average: Class A scored higher on average (median 64% > 58%).
2. Spread: Class A was more consistent (IQR 14% < 22%).
Question 1
[1 mark]
From a cumulative frequency graph of 80 test scores, the lower quartile (at cumulative frequency 20) is 22 and the upper quartile (at cumulative frequency 60) is 53.
Work out the interquartile range (IQR).
Worked Solution & Answer
IQR = UQ - LQ = 53 - 22 = 31 B1
Answer: 31
Question 2
[2 marks]
01020304050
The box plot shows the distribution of times (in minutes) taken by students to complete a puzzle.
Write down the median and work out the interquartile range (IQR).
Worked Solution & Answer
Median line is at 25. IQR = UQ - LQ = 35 - 15 = 20 (Range = 35). B1
Answer: Median = 25, IQR = 20
Question 3
[3 marks]
In an experiment, 60 students each completed a puzzle.
The cumulative frequency graph shows information about the times taken for the 60 students to complete the puzzle.
020406080100102030405060Time taken (seconds)Cumulativefrequency
020406080100Time taken (seconds)
For these 60 students,
[INDENT]the least time taken was 24 seconds
[INDENT]the greatest time taken was 96 seconds.
On the grid below, draw a box plot for the distribution of the times taken by the students.
Worked Solution & Answer
From CF graph: LQ (at CF=15) = 42 s, Median (at CF=30) = 54 s, UQ (at CF=45) = 64 s M2 A1
Answer: Box plot drawn with min = 24, LQ = 42, median = 54, UQ = 64, max = 96
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[3 marks]
Megan grows potatoes.
The box plot below shows information about the weights of Megan's potatoes.
20304050607080Weight (grams)Megan
(a) Is Megan correct?
Give a reason for your answer. [1 mark]
(b) Compare the distribution of the weights of Megan's potatoes with the distribution of the weights of Amy's potatoes. [2 marks]
20304050607080Weight (grams)Amy
Worked Solution & Answer
(a)
Megan: median = 57, IQR = 65 – 39 = 26, range = 72 – 23 = 49 C1
Answer (a): No, because the median weight is 57 grams (so half weigh less than 57 g, not 50 g)
(b)
Amy: median = 42, IQR = 51 – 35 = 16, range = 70 – 23 = 47. M1 C1
Answer (b): 1. The median weight of Megan's potatoes (57 g) is greater than the median weight of Amy's potatoes (42 g). 2. The interquartile range of Megan's potatoes (26 g) is greater than the IQR of Amy's potatoes (16 g) (or range 49 g vs 47 g).
Question Paper (PDF) • Mark Scheme (PDF)
Question 5
[3 marks]
The box plot shows information about the sales, in thousands of pounds (£000s), of an online store each month.
0100200300400500OnlinestoreSales (£000s)
(a) Explain why. [1 mark]
(b) On the grid below, draw a box plot for this information. [2 marks]
0100200300400500ShopSales (£000s)
Worked Solution & Answer
(a)
Online: median = 200, IQR = 350 – 160 = 190, range = 420 – 60 = 360 C1
Answer (a): Half (50%) of the data lies between the lower quartile and upper quartile, not three quarters
(b)
Shop: min = 30, LQ = 80, median = 170, UQ = 80 + 180 = 260, max = 350. M1 A1
0100200300400500ShopSales (£000s)
Answer (b): Box plot drawn with min=30, LQ=80, median=170, UQ=260, max=350
Question Paper (PDF) • Mark Scheme (PDF)
Question 6
[4 marks]
The box plot shows information about the distribution of the amounts of money spent by some male students on their holidays.
01002003004005006007008009001000Money spent (£)Malestudents
(a) Work out the interquartile range for the amounts of money spent by these male students. [2 marks]
£
(b) On the grid above, draw a box plot for the information in the table. [2 marks]
Money spent(£)Smallest60Lowerquartile180Median300Upperquartile350Largest650
Worked Solution & Answer
(a)
UQ = 330, LQ = 150 M1
⇒ IQR = 330 – 150 = £180 A1
Answer (a): £ 180
(b)
Plot at 60, 180, 300, 350, 650 M1 A1
Answer (b): Box plot drawn with whiskers at 60 and 650, box from 180 to 350, median at 300
Question Paper (PDF) • Mark Scheme (PDF)
Question 7
[5 marks]
The table shows some information about the heights of a group of adults.
least height169 cmgreatest height186 cmmedian177 cmlower quartile174 cmupper quartile180 cm
(a) On the grid, draw a box plot for the information in the table. [3 marks]
155160165170175180185190Height (cm)Adults
(b) Compare the distribution of the heights of the adults with the distribution of the heights of the teenagers. [2 marks]
155160165170175180185190Height (cm)Teenagers
Worked Solution & Answer
(a)
Adults: median = 177, IQR = 6, range = 17 M2 A1
155160165170175180185190Height (cm)Adults
Answer (a): Box plot drawn with whiskers at 169 and 186, box from 174 to 180, median at 177
(b)
Teenagers: median = 169, IQR = 6, range = 20.5 M1 C1
Answer (b): 1. On average, the adults are taller because their median height (177 cm) is greater than the teenagers' median height (169 cm).
2. The interquartile range of heights is the same for both groups (6 cm), or the range of heights for teenagers (20.5 cm) is greater than for adults (17 cm).
Question Paper (PDF) • Mark Scheme (PDF)
Question 8
[5 marks]
Mina records the speeds, in mph, of some cars on a road on Friday.
She uses her results to work out the information in this table.
Speed (mph)Lowest speed25Lower quartile35Median40Interquartile range12Range37
(a) On the grid, draw a box plot to show the information in the table. [3 marks]
Friday10203040506070Speed (mph)
(b) Compare the distribution of the speeds on Friday with the distribution of the speeds on Sunday. [2 marks]
Sunday10203040506070Speed (mph)
Worked Solution & Answer
(a)
UQ = 35 + 12 = 47, Max = 25 + 37 = 62 M2 A1
Friday10203040506070Speed (mph)
Answer (a): Box plot drawn with whiskers at 25 and 62, box from 35 to 47, and median at 40
(b)
Sunday: min=22, LQ=33, med=42, UQ=48, max=66 (IQR=15, range=44) M1 C1
Answer (b): 1. On average, speeds were higher on Sunday as the median speed on Sunday (42 mph) is greater than on Friday (40 mph). 2. Speeds were more spread out on Sunday as the interquartile range on Sunday (15 mph) is greater than on Friday (12 mph) (or range 44 mph > 37 mph).
Question Paper (PDF) • Mark Scheme (PDF)
Question 9
[5 marks]
The table shows information about the heights, in cm, of a group of Year 11 girls.
height (cm)least height154median165lower quartile161interquartile range7range20
(a) Draw a box plot for this information. [3 marks]
130140150160170180height (cm)Year 11
(b) Compare the distribution of heights of the Year 7 girls with the distribution of heights of the Year 11 girls. [2 marks]
130140150160170180height (cm)Year 7
Worked Solution & Answer
(a)
UQ = 161 + 7 = 168 cm M2
Max = 154 + 20 = 174 cm A1
130140150160170180height (cm)Year 11
Answer (a): Box plot with min 154, LQ 161, median 165, UQ 168, max 174
(b)
Compare medians in context (165 > 157.5) and IQR/range (7 < 10.5 or 20 < 24.5) M1 C1
Answer (b): On average, the Year 11 girls are taller (median 165 cm > 157.5 cm). The heights of the Year 11 girls are less spread out / more consistent (IQR 7 cm < 10.5 cm, range 20 cm < 24.5 cm).
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 AQA Nov 2023 1H Q15
[5 marks]
A race was run in 2019 and in 2020
The box plot shows information about the finishing times in 2019
1015202530Time (minutes)
(a) In 2019, what was the fastest time? [1 mark]
Answer minutes
(b) The table shows information about the finishing times in 2020
@@TABULAR0@@
Use the data to comment on each of the following statements.
• On average, times were faster in 2019 than in 2020
• Times were equally consistent in 2019 and 2020 [4 marks]
Worked Solution & Answer
(a)
Minimum whisker is at 16 minutes B1
Answer (a): Answer 16 minutes
(b)
2019 median = 22.5 minutes, which is less than 2020 median (24 minutes), so on average times were faster in 2019 (correct). M3
2019 IQR = 26 – 20 = 6 minutes and 2020 IQR = 27 – 21 = 6 minutes, so the interquartile ranges are equal and times were equally consistent C1
Answer (b): True: 2019 median (22.5 min) is lower than 2020 median (24 min)
True: 2019 IQR (26 – 20 = 6 min) equals 2020 IQR (27 – 21 = 6 min)
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 36 marks)
Box plots Worksheets Next: Combined transformations →

Grade 6 Quizzes

14 Topics
6A - Recurring decimals6B - Harder indices
6C - The product rule6D - Repeated change
6E - Triple brackets6F - Parallel and perpendicular
6G - Inequalities on graphs6H - Similar shapes (area and vol)
6J - Negative scale factors6K - Circle theorems
6L - Cumulative frequency6M - Box plots
6N - Combined transformations6P - Capture recapture