Box Plots - Worksheets, Questions and Revision

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GCSE · Statistics

S30 Box Plots

EDEXCEL 1ST0 · Calculator allowed · about 85 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Here is a list of five statistical terms used with box plots:

median, lower quartile, upper quartile, interquartile range, range

For each description (i) to (v), write down the term from the list that matches it.
(i)The value exactly in the middle of an ordered data set.(1)
(ii)The value below which the bottom quarter of the data lies.(1)
(iii)The value below which the top quarter of the data lies (i.e. 75% of the data is below it).(1)
(iv)The difference between the upper quartile and the lower quartile.(1)
(v)The difference between the maximum and the minimum values.(1)
(Total for Question 1 is 5 marks)
2
For each statement about box plots, write down whether it is True or False.
(i)The line drawn inside the box represents the median.(1)
(ii)The two ends of the box mark the minimum and the maximum values in the data set.(1)
(iii)The interquartile range is not affected by a few very small or very large extreme values in the data.(1)
(Total for Question 2 is 3 marks)
3
The box plot shows the times, in minutes, taken by a group of 40 students to complete an exam paper.
05101520253035404550 Time taken, t (minutes)
(a)Write down the median time.(1)
(b)Write down the upper quartile time.(1)
(c)Work out the range of the times.(2)
(d)Work out the interquartile range of the times.(2)
(Total for Question 3 is 6 marks)
4
The box plot shows the annual salaries, in £1000s, of the 60 employees at a small company.
010203040506070 Annual salary (£1000s)
(a)Write down the median annual salary.(1)
(b)Work out the range of annual salaries, giving your answer in £.(2)
(c)Work out the interquartile range of annual salaries, giving your answer in £.(2)
(d)Write down the percentage of employees who earn a salary between the lower quartile and the upper quartile.(1)
(Total for Question 4 is 6 marks)
5
The box plots show the journey times, in minutes, of two bus routes, Bus A and Bus B, recorded over several weeks.
0510152025303540455055 Journey time (minutes) Bus ABus B
(a)Write down the median journey time for Bus B.(1)
(b)Work out the interquartile range for Bus A.(2)
(c)Compare the two bus routes, using the median and the interquartile range.(3)
(Total for Question 5 is 6 marks)
6
The box plots show the monthly rainfall, in mm, recorded in City P and City Q over a year.
020406080100 Monthly rainfall (mm) City PCity Q
(a)Write down the median monthly rainfall for City P.(1)
(b)Work out the range of monthly rainfall for City Q.(2)
(c)Compare the typical rainfall and the spread of rainfall in the two cities, using the median and the range.(2)
(Total for Question 6 is 5 marks)
7
The five-number summary for the heights, in cm, of 20 sunflowers grown by a gardening club is given in the table.
MinimumLower quartileMedianUpper quartileMaximum
4055688095

On the grid, draw a box plot to show this information.
0102030405060708090100 Height (cm)
(Total for Question 7 is 3 marks)
8
The weights, in kg, of 11 parcels sent by a courier are shown below, in order:

2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 12
(a)Find the median, the lower quartile and the upper quartile of the weights.(3)
(b)On the grid provided, draw a box plot to show this data.(3)
02468101214 Weight (kg)
(Total for Question 8 is 6 marks)
9
A student wants to investigate whether Year 11 students spend more time than Year 10 students on homework each week.
(a)Write a suitable hypothesis for the student's investigation.(1)
(b)Give one thing the student should keep the same for both year groups when collecting the data, so that the comparison is fair.(1)
(c)The student collects the data and summarises it using the two box plots shown, for time spent on homework (hours per week).

Compare the amount of time spent on homework by Year 10 and Year 11, using the median and the interquartile range.(3)
048121620 Time spent on homework (hours per week) Year 10Year 11
(d)State whether the student's data supports the hypothesis from part (a).(1)
(Total for Question 9 is 6 marks)
10
The box plot shows the amount of time, in minutes, that 50 customers spent in a shop.
051015202530 Time spent in shop (minutes)
(Total for Question 10 is 3 marks)
11
The box plot shows the finishing times, in seconds, of 30 runners in a sprint race. One runner's time, 52 seconds, is much slower than the rest and is plotted as a separate circle beyond the whisker, because it is an outlier.

A value is classed as an outlier if it is more than 1.5 x IQR above the upper quartile, or more than 1.5 x IQR below the lower quartile.
0102030405060 Finishing time (seconds)
(a)Show that 52 seconds is an outlier.(2)
(b)Write down the value that the upper whisker of the box plot is drawn to.(1)
(c)Write down the least finishing time recorded in the race.(1)
(Total for Question 11 is 4 marks)
12
The times, in minutes, taken by 13 people to complete a charity fun run are shown below, in order:

32, 35, 36, 38, 39, 40, 41, 42, 44, 45, 47, 48, 71
(a)Write down the median time.(1)
(b)Work out the lower quartile.(2)
(c)Work out the upper quartile.(2)
(d)Work out the interquartile range.(1)
(e)A value is an outlier if it is more than 1.5 x IQR above the upper quartile. Show that 71 minutes is an outlier.(2)
(f)State the value that the upper whisker of a box plot for this data would be drawn to.(1)
(Total for Question 12 is 9 marks)
13
The box plots show two distributions, X and Y, plotted on the same scale.
05101520253035 Value XY
(a)State whether Distribution X is positively skewed, negatively skewed, or symmetrical. Give a reason based on the position of the median within the box.(2)
(b)State whether Distribution Y is positively skewed, negatively skewed, or symmetrical. Give a reason based on the position of the median within the box.(2)
(Total for Question 13 is 4 marks)
14
60 students took a puzzle-solving test. The grouped frequency table shows their completion times.
Time, t (minutes)Frequency
0 < t ≤ 205
20 < t ≤ 4015
40 < t ≤ 6025
60 < t ≤ 8010
80 < t ≤ 1005

The cumulative frequency graph for this data is shown below.
020406080100 0102030405060 Time, t (minutes) Cumulative frequency
(a)Use the graph to find an estimate for the median completion time.(1)
(b)Use the graph to find estimates for the lower quartile and the upper quartile.(2)
(c)Work out an estimate for the interquartile range.(1)
(d)Given that the fastest student finished in 10 minutes and the slowest student finished in 95 minutes, draw a box plot to show this information, using your estimates from parts (a) and (b).(3)
0102030405060708090100 Time, t (minutes)
(Total for Question 14 is 7 marks)
15
The box plots show the distances thrown, in metres, by three javelin throwers, A, B and C, over a season of competitions.
01020304050 Distance thrown (metres) ABC
(a)Work out the interquartile range for each thrower.(3)
(b)Which thrower was the most consistent? Give a reason.(1)
(c)Describe the skewness of Thrower B's distribution, giving a reason based on the box plot.(2)
(Total for Question 15 is 6 marks)
Mark scheme · S30 Box Plots

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15