Box Plots: Fluency and Exam Drill - Worksheets, Questions and Revision

22 original exam-style questions - 11 pages of questions with a full mark scheme - free printable PDF.

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6.12D Box Plots: Fluency and Exam Drill

EDEXCEL 1MA1 · Calculators not allowed · about 80 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
This question checks some key facts about box plots.
(a)Write down the name given to the difference between the upper quartile and the lower quartile of a data set.(1)
(b)A box plot is drawn using five statistics, often called the five-number summary. Write down all five of these statistics.(1)
(Total for Question 1 is 2 marks)
2
Eshaal recorded the number of minutes she spent practising the guitar on 7 days last week. The times, already written in order, were:

10, 15, 15, 20, 25, 30, 40
(a)Write down the median practice time.(1)
(b)Work out the range of practice times.(1)
(Total for Question 2 is 2 marks)
3
A book club recorded the number of pages read last week by each of its 8 members, listed in order:

45, 52, 58, 60, 65, 70, 74, 81
(a)Find the median number of pages read.(1)
(b)Find the lower quartile.(1)
(c)Find the upper quartile.(1)
(Total for Question 3 is 3 marks)
4
The midday temperature, in degrees C, was recorded on 9 consecutive days in March, listed in order:

6, 8, 8, 9, 11, 13, 14, 16, 19
(a)Find the median temperature.(1)
(b)Find the lower quartile.(1)
(c)Find the upper quartile.(1)
(Total for Question 4 is 3 marks)
5
Using your answers to Question 4, work out the following for the midday temperatures.
(a)Work out the range of temperatures.(1)
(b)Work out the interquartile range of temperatures.(1)
(Total for Question 5 is 2 marks)
6
The box plot shows the distance, in km, cycled by 60 members of a cycling club last Saturday.
Distance cycled (km) by 60 cycling club members 0 5 10 15 20 25 30 35 40 45 Distance cycled (km)
(a)Write down the median distance cycled.(1)
(b)Write down the interquartile range of the distances.(1)
(c)Write down the range of the distances.(1)
(d)Work out the number of members who cycled more than 28 km.(1)
(Total for Question 6 is 4 marks)
7
A recipe website recorded the preparation time, in minutes, taken by 200 users to make the same lasagne recipe. The five-number summary is:

Minimum = 10, Lower quartile = 25, Median = 35, Upper quartile = 50, Maximum = 90
(a)Write down the interquartile range of the preparation times.(1)
(b)Write down the range of the preparation times.(1)
(c)One user takes 65 minutes to prepare the lasagne. State, with a reason, whether this user is in the slowest 25% of users.(1)
(Total for Question 7 is 3 marks)
8
The five-number summary for the mass, in kg, of 45 parcels processed at a delivery depot is:

Minimum = 2, Lower quartile = 6, Median = 9, Upper quartile = 14, Maximum = 20

On the grid provided, draw a box plot for this data.
Mass of parcels (kg) - grid for your box plot 0 4 8 12 16 20 Mass of parcel (kg)
(Total for Question 8 is 4 marks)
9
A class survey recorded the number of siblings reported by 11 students, listed in order:

0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 5
(a)Find the median number of siblings.(1)
(b)Find the lower quartile.(1)
(c)Find the upper quartile.(1)
(Total for Question 9 is 3 marks)
10
Using your answers to Question 9, work out the following for the number of siblings.
(a)Work out the range.(1)
(b)Work out the interquartile range.(1)
(Total for Question 10 is 2 marks)
11
The box plot shows the scores, out of 40, of 32 students in a spelling test.
Spelling test scores (out of 40) for 32 students 0 5 10 15 20 25 30 35 40 Test score (out of 40)
(a)Write down the median score.(1)
(b)Work out the range of scores.(1)
(Total for Question 11 is 2 marks)
12
A cafe measures the waiting time for coffee orders on a busy Saturday morning and on a quiet Tuesday morning. On the busy Saturday, the interquartile range of waiting times is 6 minutes. On the quiet Tuesday, the interquartile range of waiting times is 2 minutes.
(Total for Question 12 is 2 marks)
13
Priya, a gardener, recorded the height, in cm, of 15 tomato plants. The five-number summary is:

Minimum = 30, Lower quartile = 45, Median = 55, Upper quartile = 68, Maximum = 140
(a)Work out the interquartile range of the plant heights.(1)
(b)The maximum height of 140 cm is much larger than the rest of the data. Suggest one reason why this value might not be typical of the tomato plants.(1)
(Total for Question 13 is 2 marks)
14
Box plots are a common way of displaying data.
(a)State one advantage of displaying data as a box plot rather than as a list of raw values.(1)
(b)State one piece of information about the data set that is lost when it is displayed as a box plot instead of the original list of values.(1)
(Total for Question 14 is 2 marks)
15
Two rival bus routes, the 24 and the 58, were compared by recording the journey time, in minutes, for 40 journeys on each route one weekday morning. The box plots show the results.

Route 24: minimum = 18, lower quartile = 24, median = 30, upper quartile = 38, maximum = 50
Route 58: minimum = 15, lower quartile = 20, median = 33, upper quartile = 36, maximum = 55
Journey time (minutes): Route 24 and Route 58 24 58 0 5 10 15 20 25 30 35 40 45 50 55 Journey time (minutes)
(a)Write down the median journey time for each route.(2)
(b)By comparing the interquartile ranges, compare the consistency of journey times on the two routes.(2)
(Total for Question 15 is 4 marks)
16
A school entered 84 pupils for a mock exam. The exam scores are summarised by: minimum = 20, lower quartile = 48, median = 60, upper quartile = 75, maximum = 98. Pupils who score above the upper quartile are awarded a distinction certificate. Pupils who score below the lower quartile are given extra revision support.
(a)Work out how many pupils receive a distinction certificate.(1)
(b)Work out how many pupils are NOT given extra revision support.(2)
(Total for Question 16 is 3 marks)
17
Kwame, a private tutor, recorded the length, in minutes, of 15 one-to-one tutoring sessions, listed in order:

25, 28, 30, 30, 32, 35, 36, 38, 40, 42, 44, 45, 48, 50, 65
(a)Find the median length of a session.(1)
(b)Find the lower quartile and the upper quartile of the session lengths.(2)
(c)Kwame uses the rule that a session length is an outlier if it is more than 1.5 x IQR above the upper quartile. Determine, showing your working, whether the 65-minute session is an outlier.(2)
(Total for Question 17 is 5 marks)
18
The delivery times, in days, for 500 online orders have the five-number summary:

Minimum = 1, Lower quartile = 3, Median = 4, Upper quartile = 9, Maximum = 20
(a)Work out the distance from the lower quartile to the median, and the distance from the median to the upper quartile.(1)
(b)Using your answer to part (a), state whether the distribution of delivery times is more likely to be positively skewed (a small number of unusually long delivery times stretching the distribution) or negatively skewed, giving a reason.(2)
(c)Suggest one possible reason, in context, for this pattern in delivery times.(1)
(Total for Question 18 is 4 marks)
19
A factory tests the breaking strength, in Newtons, of 200 rope samples this year and 200 rope samples from last year.

This year: minimum = 310, lower quartile = 395, median = 430, upper quartile = 470, maximum = 620
Last year: minimum = 290, lower quartile = 380, median = 425, upper quartile = 460, maximum = 520
(a)Work out the interquartile range of the breaking strengths for each year.(2)
(b)The factory claims: 'Our ropes have become more consistent in strength this year.' Using your answer to part (a), and one other valid comparison from the data, evaluate this claim.(2)
(Total for Question 19 is 4 marks)
20
The five-number summary for the finishing times, in minutes, of 400 runners in a fun run is:

Minimum = 28, Lower quartile = 42, Median = 50, Upper quartile = 64, Maximum = 95

A runner finishes in 57 minutes. Assuming finishing times are evenly spread within each quarter of the data, estimate the percentage of runners who finished in under 57 minutes.
(Total for Question 20 is 3 marks)
21
A statistician summarises a data set of 120 values. The lower quartile is 12. The median is x, and the upper quartile is (3x - 8). The interquartile range of the data set is 34. Separately, it is known that the minimum value in the data set is 5 and the maximum is 90.
(a)Form an equation in x for the interquartile range, and solve it to find the median.(3)
(b)Write down the upper quartile of the data set.(1)
(c)Work out the number of values in the data set that lie between the median and the maximum.(1)
(d)Write down the range of the data set.(1)
(Total for Question 21 is 6 marks)
22
A company tests the battery life, in hours, of two models of wireless earbuds, using a sample of 200 units of each model.

Model A: minimum = 8, lower quartile = 14, median = 18, upper quartile = 24, maximum = 30

Model B has the same median and the same range as Model A. Model B's interquartile range is exactly 3 hours smaller than Model A's, and Model B's lower quartile is 2 hours higher than Model A's lower quartile.
(a)Work out the interquartile range of Model A.(1)
(b)Work out the interquartile range of Model B.(1)
(c)Work out the lower quartile and the upper quartile of Model B.(2)
(d)A marketing claim states: 'Model B's battery life is more consistent, and at least as long-lasting, as Model A's.' Using your answers, and the fact that both models share the same median and range, evaluate this claim.(1)
(Total for Question 22 is 5 marks)
Mark scheme · 6.12D Box Plots: Fluency and Exam Drill

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

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22