The table gives information about the times, in minutes, that 51 patients waited at a clinic.
Shortest time
15
Lower quartile
22
Median
38
Upper quartile
46
Longest time
63
Tom draws a box plot for this information. On his box plot:
the left whisker ends at 12
the line inside the box is drawn at 34
Write down two things that are wrong with Tom's box plot.
2 marks
Show answer
The left whisker should end at 15 (the shortest time), not 12; the median line should be at 38, not 34
2
The box plot shows the journey times, in minutes, of 15 deliveries made by a courier.
Write down the median journey time.
Work out the interquartile range of the journey times.
Work out the range of the journey times.
3 marks
Show answer
a) 19 minutesb) 12 minutesc) 26 minutes
3
Here are the scores of 15 pupils in a spelling test, shown in a stem and leaf diagram.
Stem
Leaf
2
3 5 8
3
1 4 4 7
4
0 2 5 6
5
1 3 8
6
0
Key: 2 | 3 means a score of 23
Write down the five values needed to draw a box plot: the minimum, lower quartile, median, upper quartile and maximum.
Draw a box plot for these scores on a scale from 20 to 60.
3 marks
Show answer
a) minimum 23, lower quartile 31, median 40, upper quartile 51, maximum 60b) box from 31 to 51, median line at 40, whiskers to 23 and 60
4
Here are the numbers of emails Priya received on each of 11 days, written in order.
3 5 6 8 9 11 13 14 16 18 21
Find the median.
Find the lower quartile and the upper quartile.
Work out the interquartile range.
3 marks
Show answer
a) 11b) lower quartile 6, upper quartile 16c) 10
5
A box plot shows the times, in minutes, that 120 pupils took to complete a puzzle. The five values on the box plot are:
Minimum
12
Lower quartile
18
Median
25
Upper quartile
34
Maximum
50
Work out the range and the interquartile range.
What percentage of the pupils took between 18 and 34 minutes?
Estimate how many pupils took more than 34 minutes.
4 marks
Show answer
a) range 38, interquartile range 16b) 50%c) 30
6
The stem and leaf diagram shows the marks of 15 students in a spelling test.
Stem
Leaves
1
2 5 8
2
0 3 4 7 9
3
1 4 6 8
4
0 2 5
Key: 2 | 3 means 23 marks
Work out the five values needed to draw a box plot for this data: the lowest mark, the lower quartile, the median, the upper quartile and the highest mark.
The cumulative frequency graph for 40 journey times, in minutes, shows that the shortest journey took 5 minutes, the 10th journey took 12 minutes, the 20th took 18 minutes, the 30th took 25 minutes and the longest took 41 minutes.
Write down the minimum, lower quartile, median, upper quartile and maximum.
Draw a box plot for the journey times.
Estimate how many journeys took between 12 and 25 minutes.
5 marks
Show answer
a) 5, 12, 18, 25, 41b) box from 12 to 25, median line at 18, whiskers to 5 and 41c) 20
8
Two Year 11 classes sat the same test. The box plots for their marks have these five values.
Minimum
Lower quartile
Median
Upper quartile
Maximum
Class A
20
38
50
62
90
Class B
31
45
54
60
78
Compare the marks of the two classes. Use the medians and the interquartile ranges, and refer to the context.
4 marks
Show answer
Class B had the higher median (54 against 50), so typically scored higher. Class B had the smaller interquartile range (15 against 24), so its marks were more consistent.
9
Two shops sell second-hand bikes. The tables summarise the prices, in pounds, of the bikes sold last month.
Shop A
Minimum
60
Lower quartile
95
Median
130
Upper quartile
180
Maximum
250
Shop B: median £150, interquartile range £45.
Work out the interquartile range of the prices at Shop A.
Compare the prices of bikes at the two shops. Give two comparisons.
Which shop has the more consistent prices? Give a reason.
4 marks
Show answer
a) £85b) Shop B has the higher median so its bikes cost more on average; Shop A has the larger IQR so its prices vary morec) Shop B - smaller interquartile range means more consistent prices
10
60 students sat a mock exam. The lowest mark was 8 and the highest was 59. The lower quartile was 21, the median was 34 and the upper quartile was 47.
Draw a box plot for the marks on a scale from 0 to 60.
Estimate the number of students who scored more than 21.
Estimate the number of students who scored between 34 and 47.
4 marks
Show answer
a) box from 21 to 47, median line at 34, whiskers to 8 and 59b) 45c) 15
11
A box plot summarises the times, in minutes, taken by 120 runners to finish a 10 km race.
On the box plot: the whiskers are at 22 and 58, the box goes from 28 to 41, and the median line is at 33.
Work out the interquartile range of the times.
Estimate how many of the 120 runners took longer than 41 minutes.
Explain why your answer to part (b) is an estimate.
4 marks
Show answer
a) 13 minutesb) 30c) A box plot gives only a five-number summary, so we assume exactly a quarter of the runners are above the upper quartile
12
The table gives information about the times, in minutes, that the girls in a class spent on homework one evening.
Shortest time
5
Lower quartile
9
Median
12
Upper quartile
15
Longest time
22
On the grid, draw a box plot for this information.
The box plot for the boys in the class is shown on the same grid. The boys had a median of 14 minutes and an interquartile range of 8 minutes. Compare the times spent by the girls and the boys. Give two comparisons.
5 marks
Show answer
a) whiskers at 5 and 22, box 9 to 15, median at 12b) Girls' median lower (12 vs 14) so girls spent less time on average; girls' IQR smaller (6 vs 8) so girls' times were more consistent
13
A weather station recorded the daily rainfall, in mm, on each of 60 days.
The lowest rainfall was 2 mm.
The range was 30 mm.
The median was 15 mm.
The lower quartile was 10 mm.
The interquartile range was 12 mm.
Use this information to draw a box plot for the rainfall.
Estimate the number of days on which the rainfall was more than 22 mm.
5 marks
Show answer
a) whiskers at 2 and 32, box 10 to 22, median at 15b) 15
14
The cumulative frequency graph shows the weights, in kg, of 80 parcels sent from a depot on Monday.
The lightest parcel weighed 0.5 kg and the heaviest weighed 9.5 kg.
Use the graph to draw a box plot for the weights of Monday's parcels.
Use the graph to estimate the number of parcels that weighed more than 7 kg.
On Tuesday the parcels had a median weight of 4.4 kg and an interquartile range of 2.1 kg. Compare the weights of Monday's and Tuesday's parcels.
6 marks
Show answer
a) min 0.5, LQ approximately 3.75 (accept 3.5-4), median approximately 5.2 (accept 5-5.4), UQ approximately 6.8 (accept 6.5-7.1), max 9.5b) approximately 18 (accept 15-21)c) Monday's median is higher so Monday's parcels were heavier on average; Monday's IQR is larger so Monday's weights varied more
15
Here are the times, in seconds, taken by the 15 swimmers in Team A to swim 50 metres.
41 38 45 36 50 39 43 47 35 44 40 52 37 46 42
Find the median, the lower quartile and the upper quartile of the times for Team A.
Team B's times had a median of 44 seconds and an interquartile range of 13 seconds. Compare the times of the two teams. Give two comparisons.
5 marks
Show answer
a) median 42, lower quartile 38, upper quartile 46b) Team A has the lower median so was faster on average; Team A has the smaller IQR so was more consistent
16
The table summarises the battery life, in hours, of 80 phones of Model X.
Minimum
8
Lower quartile
13
Median
16
Upper quartile
20
Maximum
27
Jay tries to draw a box plot for Model X. On his diagram the whiskers are at 13 and 20 and the box goes from 8 to 27 with a line at 16.
Write down two mistakes Jay has made.
On the grid, draw a correct box plot for Model X.
The box plot for Model Y is drawn on the same grid. Model Y has a median of 15 hours and an interquartile range of 4 hours. Compare the battery lives of the two models.
5 marks
Show answer
a) Box drawn between min and max instead of between the quartiles; whiskers drawn at the quartiles instead of at min and maxb) whiskers at 8 and 27, box 13 to 20, median at 16c) Model X has the higher median so lasts longer on average; Model X has the larger IQR so is less consistent
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.