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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
A call centre recorded how long each of 160 customers waited before their call was answered. The cumulative frequency diagram shows the results.
2
4
6
8
10
20
40
60
80
100
120
140
160
Waiting time (minutes)
Cumulative frequency
(a)
Use the diagram to estimate the number of customers who waited between 3 minutes and 7 minutes.
(b)
The call centre claims that 80% of its customers wait less than 6 minutes. Use the diagram to decide whether this claim is correct. You must show your working.
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Level 4
6 marks
Start
→
Mark as done
The table shows the masses of 50 pumpkins grown on a farm.
Mass,
m
m
m
(kg)
Frequency
0
<
m
≤
4
0 < m \le 4
0
<
m
≤
4
4
4
<
m
≤
8
4 < m \le 8
4
<
m
≤
8
11
8
<
m
≤
12
8 < m \le 12
8
<
m
≤
12
18
12
<
m
≤
16
12 < m \le 16
12
<
m
≤
16
12
16
<
m
≤
20
16 < m \le 20
16
<
m
≤
20
5
(a)
Write down the cumulative frequency for each of the five classes.
Bella draws a cumulative frequency diagram for this information. She plots each of her points at the midpoint of its class, so her curve ends at a mass of
18
18
18
kg.
(b)
Explain what Bella's diagram wrongly claims about the heaviest pumpkin.
(c)
Write down the coordinates of the point at which Bella's curve should have ended.
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Level 4
4 marks
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Mark as done
The cumulative frequency diagram shows the heights of 200 trees in a wood.
5
10
15
20
25
50
100
150
200
Height (metres)
Cumulative frequency
(a)
Use the diagram to estimate the median height of the trees.
(b)
Use the diagram to estimate the number of trees that are taller than 12 m.
(c)
Explain why your answer to part (b) is only an estimate.
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Level 4
6 marks
Start
→
Mark as done
The frequency table gives information about the times, in minutes, that
120
120
120
runners took to complete a fun run.
Time (
t
t
t
minutes)
Frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
8
8
8
25
<
t
≤
30
25 < t \le 30
25
<
t
≤
30
22
22
22
30
<
t
≤
35
30 < t \le 35
30
<
t
≤
35
46
46
46
35
<
t
≤
40
35 < t \le 40
35
<
t
≤
40
30
30
30
40
<
t
≤
45
40 < t \le 45
40
<
t
≤
45
14
14
14
(a)
Complete the cumulative frequency table.
Time (
t
t
t
minutes)
Cumulative frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
20
<
t
≤
30
20 < t \le 30
20
<
t
≤
30
20
<
t
≤
35
20 < t \le 35
20
<
t
≤
35
20
<
t
≤
40
20 < t \le 40
20
<
t
≤
40
20
<
t
≤
45
20 < t \le 45
20
<
t
≤
45
(1 mark)
(b)
On the grid, draw a cumulative frequency graph for your table.
20
25
30
35
40
45
20
40
60
80
100
120
Time (t minutes)
Cumulative frequency
(2 marks)
(c)
Use your graph to find an estimate for the interquartile range.
(2 marks)
(d)
Use your graph to find an estimate for the number of these runners who took more than
38
38
38
minutes.
(2 marks)
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Level 4
7 marks
Start
→
Quartiles & the interquartile range
14 questions
Lesson
Not started
Mark as done
The cumulative frequency diagram shows the heights of 200 trees in a wood.
5
10
15
20
25
50
100
150
200
Height (metres)
Cumulative frequency
(a)
Use the diagram to estimate the median height of the trees.
(b)
Use the diagram to estimate the number of trees that are taller than 12 m.
(c)
Explain why your answer to part (b) is only an estimate.
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Level 4
6 marks
Start
→
Mark as done
Class A and class B were each given the same puzzle to solve.
The cumulative frequency diagram shows the time, in seconds, taken by each of the
60
60
60
pupils in class A.
10
20
30
40
50
10
20
30
40
50
60
Time (seconds)
Cumulative frequency
(a)
Use the diagram to estimate the median time for class A.
(b)
Use the diagram to estimate the interquartile range of the times for class A.
(c)
For class B, the median time was
34
34
34
seconds and the interquartile range was
21
21
21
seconds.
Compare the times taken by class A with the times taken by class B.
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Level 4
7 marks
Start
→
Mark as done
Nine numbers are written in order of size:
4
,
7
,
9
,
11
,
14
,
16
,
x
,
21
,
28
4, \quad 7, \quad 9, \quad 11, \quad 14, \quad 16, \quad x, \quad 21, \quad 28
4
,
7
,
9
,
11
,
14
,
16
,
x
,
21
,
28
The interquartile range of the nine numbers is
12
12
12
.
(a)
Write down the median of the nine numbers.
(b)
Work out the value of
x
x
x
.
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Level 4
4 marks
Start
→
Mark as done
A shop recorded the amount spent by each of
15
15
15
customers one morning. The amounts, in pounds, were:
12
,
27
,
5
,
17
,
9
,
68
,
14
,
3
,
22
,
8
,
19
,
6
,
24
,
11
,
15
12, \quad 27, \quad 5, \quad 17, \quad 9, \quad 68, \quad 14, \quad 3, \quad 22, \quad 8, \quad 19, \quad 6, \quad 24, \quad 11, \quad 15
12
,
27
,
5
,
17
,
9
,
68
,
14
,
3
,
22
,
8
,
19
,
6
,
24
,
11
,
15
(a)
Work out the interquartile range of the amounts spent.
(b)
Ravi says, "The range of the amounts is £
65
65
65
, so the amounts spent that morning were very spread out."
Explain why the interquartile range gives a more reliable picture of the spread of these amounts than the range does.
●●●●
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Level 4
5 marks
Start
→
Mark as done
The frequency table gives information about the times, in minutes, that
120
120
120
runners took to complete a fun run.
Time (
t
t
t
minutes)
Frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
8
8
8
25
<
t
≤
30
25 < t \le 30
25
<
t
≤
30
22
22
22
30
<
t
≤
35
30 < t \le 35
30
<
t
≤
35
46
46
46
35
<
t
≤
40
35 < t \le 40
35
<
t
≤
40
30
30
30
40
<
t
≤
45
40 < t \le 45
40
<
t
≤
45
14
14
14
(a)
Complete the cumulative frequency table.
Time (
t
t
t
minutes)
Cumulative frequency
20
<
t
≤
25
20 < t \le 25
20
<
t
≤
25
20
<
t
≤
30
20 < t \le 30
20
<
t
≤
30
20
<
t
≤
35
20 < t \le 35
20
<
t
≤
35
20
<
t
≤
40
20 < t \le 40
20
<
t
≤
40
20
<
t
≤
45
20 < t \le 45
20
<
t
≤
45
(1 mark)
(b)
On the grid, draw a cumulative frequency graph for your table.
20
25
30
35
40
45
20
40
60
80
100
120
Time (t minutes)
Cumulative frequency
(2 marks)
(c)
Use your graph to find an estimate for the interquartile range.
(2 marks)
(d)
Use your graph to find an estimate for the number of these runners who took more than
38
38
38
minutes.
(2 marks)
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Level 4
7 marks
Start
→
Mark as done
Ravi measures the lengths, in cm, of some fish caught in a lake in June.
His results are summarised in this table.
Length (cm)
Shortest length
18
18
18
Lower quartile
24
24
24
Median
29
29
29
Interquartile range
9
9
9
Range
26
26
26
(a)
On the grid, draw a box plot to show the information in the table.
June
15
20
25
30
35
40
45
50
Length (cm)
(3 marks)
Ravi also measures the lengths of some fish caught in the lake in September.
He uses his results to draw this box plot.
September
15
20
25
30
35
40
45
50
Length (cm)
(b)
Compare the distribution of the lengths of the fish caught in June with the distribution of the lengths of the fish caught in September.
(2 marks)
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Level 4
5 marks
Start
→
Box plots
12 questions
Lesson
Not started
Mark as done
The box plots give information about the marks scored in the same test by the students at School P and by the students at School Q.
School P:
10
20
30
40
50
60
70
Mark
School Q:
10
20
30
40
50
60
70
Mark
(a)
Compare the distribution of the marks at School P with the distribution of the marks at School Q.
(b)
160
160
160
students at School P took the test. Work out how many of them scored more than
50
50
50
marks.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The box plot gives information about the times, in minutes, that
80
80
80
customers spent in a café one afternoon. One of the times is shown as a cross.
10
20
30
40
50
60
70
80
Time (minutes)
(a)
Write down the longest of these times that is
not
an outlier.
(b)
Work out the interquartile range of the times.
(c)
Zak says, "The range of these times is
35
35
35
minutes."
Explain why Zak is wrong.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The cumulative frequency graph gives information about the marks scored by
80
80
80
students in a test.
10
20
30
40
50
60
70
10
20
30
40
50
60
70
80
Mark
Cumulative frequency
The lowest mark scored was
12
12
12
and the highest mark scored was
68
68
68
.
(a)
Use the graph to draw a box plot for the marks.
(b)
Work out the interquartile range of the marks.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Ravi measures the lengths, in cm, of some fish caught in a lake in June.
His results are summarised in this table.
Length (cm)
Shortest length
18
18
18
Lower quartile
24
24
24
Median
29
29
29
Interquartile range
9
9
9
Range
26
26
26
(a)
On the grid, draw a box plot to show the information in the table.
June
15
20
25
30
35
40
45
50
Length (cm)
(3 marks)
Ravi also measures the lengths of some fish caught in the lake in September.
He uses his results to draw this box plot.
September
15
20
25
30
35
40
45
50
Length (cm)
(b)
Compare the distribution of the lengths of the fish caught in June with the distribution of the lengths of the fish caught in September.
(2 marks)
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Level 4
5 marks
Start
→
Mark as done
The table gives some information about the lengths, in minutes, of
60
60
60
films shown at a film festival.
Length (minutes)
Shortest length
84
84
84
Longest length
152
152
152
Lower quartile
97
97
97
Upper quartile
121
121
121
Median
108
108
108
(a)
Draw a box plot to represent this information.
80
90
100
110
120
130
140
150
160
Length (minutes)
(3 marks)
(b)
Work out an estimate for the number of these films with a length between
97
97
97
minutes and
121
121
121
minutes.
(1 mark)
Oscar says,
"The median is
108
108
108
minutes, so one of the films must be exactly
108
108
108
minutes long."
(c)
Is Oscar correct? Give a reason for your answer.
(1 mark)
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Level 4
5 marks
Start
→