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31 questions at your level
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Level 2
Level 3
Level 4
Level 5
Cumulative frequency diagrams
11 questions
Lesson
Not started
Mark as done
The table shows the amounts spent in one week by 80 shoppers at a supermarket.
Amount spent,
x
x
x
(£)
Frequency
0
<
x
≤
20
0 < x \le 20
0
<
x
≤
20
8
20
<
x
≤
40
20 < x \le 40
20
<
x
≤
40
22
40
<
x
≤
60
40 < x \le 60
40
<
x
≤
60
26
60
<
x
≤
80
60 < x \le 80
60
<
x
≤
80
17
80
<
x
≤
100
80 < x \le 100
80
<
x
≤
100
7
(a)
Write down the cumulative frequency for each of the five classes.
(b)
Draw a cumulative frequency diagram for this information.
(c)
Use your diagram to estimate the number of shoppers who spent £50 or less.
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Level 3
5 marks
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The cumulative frequency diagram shows the number of hours that each of 100 students spent revising in one month.
5
10
15
20
25
20
40
60
80
100
Revision time (hours)
Cumulative frequency
(a)
Use the diagram to estimate the number of students who revised for 12 hours or less.
(b)
75
75
75
of the students revised for less than
h
h
h
hours. Use the diagram to estimate the value of
h
h
h
.
(c)
Explain why your answer to part (a) can only be an estimate.
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Level 3
5 marks
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The cumulative frequency graph gives information about the times, in minutes, that
60
60
60
students took to finish a puzzle.
5
10
15
20
25
30
35
40
10
20
30
40
50
60
Time (minutes)
Cumulative frequency
(a)
Use the graph to find an estimate for the median time. (1 mark)
(b)
Use the graph to find an estimate for the interquartile range of the times. (2 marks)
(c)
Use the graph to find an estimate for the number of students who took longer than
25
25
25
minutes. (1 mark)
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Level 3
4 marks
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The cumulative frequency graph shows the times, in minutes, taken by
80
80
80
students to travel to school.
10
20
30
40
50
60
10
20
30
40
50
60
70
80
Time (minutes)
Cumulative frequency
(a)
Estimate the median time. [1]
(b)
Estimate the interquartile range. [2]
(c)
Estimate the number of students who took longer than
45
45
45
minutes. [1]
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Level 3
4 marks
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Quartiles & the interquartile range
14 questions
Lesson
Not started
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Sasha recorded the time, in seconds, that each of
13
13
13
people took to solve a puzzle. Here are her results:
32
,
18
,
45
,
27
,
21
,
38
,
25
,
30
,
22
,
36
,
28
,
41
,
24
32, \quad 18, \quad 45, \quad 27, \quad 21, \quad 38, \quad 25, \quad 30, \quad 22, \quad 36, \quad 28, \quad 41, \quad 24
32
,
18
,
45
,
27
,
21
,
38
,
25
,
30
,
22
,
36
,
28
,
41
,
24
(a)
Work out the interquartile range of these times.
(b)
Sasha then finds that the time of
45
45
45
seconds was written down wrongly. It should have been
145
145
145
seconds.
State the effect this correction has on the range and on the interquartile range of the times. Give a reason for your answer.
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Level 3
5 marks
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The cumulative frequency diagram shows the time, in minutes, that each of
80
80
80
patients waited to be seen at a clinic.
10
20
30
40
50
60
10
20
30
40
50
60
70
80
Waiting time (minutes)
Cumulative frequency
(a)
Use the diagram to estimate the median waiting time.
(b)
Use the diagram to estimate the interquartile range of the waiting times.
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Level 3
5 marks
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Mark as done
The cumulative frequency graph gives information about the times, in minutes, that
60
60
60
students took to finish a puzzle.
5
10
15
20
25
30
35
40
10
20
30
40
50
60
Time (minutes)
Cumulative frequency
(a)
Use the graph to find an estimate for the median time. (1 mark)
(b)
Use the graph to find an estimate for the interquartile range of the times. (2 marks)
(c)
Use the graph to find an estimate for the number of students who took longer than
25
25
25
minutes. (1 mark)
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Level 3
4 marks
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Mark as done
The cumulative frequency graph shows the times, in minutes, taken by
80
80
80
students to travel to school.
10
20
30
40
50
60
10
20
30
40
50
60
70
80
Time (minutes)
Cumulative frequency
(a)
Estimate the median time. [1]
(b)
Estimate the interquartile range. [2]
(c)
Estimate the number of students who took longer than
45
45
45
minutes. [1]
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Level 3
4 marks
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Box plots
12 questions
Lesson
Not started
Mark as done
A gardener measures the heights of
40
40
40
sunflowers.
The shortest sunflower is
84
84
84
cm tall and the tallest is
186
186
186
cm tall.
The median height is
120
120
120
cm, the lower quartile is
108
108
108
cm and the upper quartile is
156
156
156
cm.
(a)
Draw a box plot for this information.
(b)
Work out the interquartile range of the heights.
(c)
Work out how many of the sunflowers are taller than
156
156
156
cm.
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Level 3
5 marks
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The box plot gives information about the times, in minutes, taken by
200
200
200
people to travel to work.
10
20
30
40
50
60
70
Time (minutes)
(a)
Work out the interquartile range of the times.
(b)
Priya looks at the box plot and says, "Most of these people took between
35
35
35
and
60
60
60
minutes to travel to work, because that part of the box plot is much longer than any other part."
Is Priya correct? Give a reason for your answer.
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Level 3
4 marks
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The box plot shows information about the times, in minutes, that students in class A took to finish a test.
10
20
30
40
50
Time (minutes)
(a)
Write down the interquartile range for class A. (1 mark)
For class B: the shortest time was
12
12
12
minutes, the lower quartile was
20
20
20
minutes, the median was
26
26
26
minutes, the upper quartile was
33
33
33
minutes and the longest time was
40
40
40
minutes.
(b)
Compare the distribution of the times for class A with the distribution of the times for class B. (2 marks)
(c)
What fraction of the students in class A took longer than
30
30
30
minutes? (1 mark)
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Level 3
4 marks
Start
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