CUMULATIVE
FREQUENCY
Name: _______________________
Total Marks: ___________
Q.
1
2
3
4
5
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Max Actual RAG
4
5
2
6
6
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Q1. The weight, in kg, of 50 people in a club was recorded. The cumulative
frequency graph shows these results.
a) Using the cumulative frequency graph, find an estimate for
i.
The median
ii.
The inter-quartile range.
b) Write down the percentage of the weights represented by the interquartile range.
(4 marks)
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©JustMaths 2013
Q2. The table shows information about the speeds of 100 lorries.
Speed (s) in km/h
Frequency
0 < s ≤ 20
2
20 < s ≤ 40
9
40 < s ≤ 60
23
60 < s ≤ 80
31
80 < s ≤ 100
27
100 < s ≤ 120
8
a) Complete the cumulative frequency table for this information.
Speed (s) in km/h
Cumulative Frequency
0 < s ≤ 20
2
0 < s ≤ 40
0 < s ≤ 60
0 < s ≤ 80
0 < s ≤ 100
0 < s ≤ 120
b) On the grid draw a cumulative frequency graph for your table.
c) Find an estimate for the number of lorries with a speed of more than
90 km/h.
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©JustMaths 2013
(5 marks)
Q3.
One Saturday an internet cafe owner recorded the time each of 100
customers spent answering emails. The table below shows a summary
of the results.
Time t, minutes
Frequency
0 < x ≤ 10
23
10 < x ≤ 20
27
20 < x ≤ 30
32
30 < x ≤ 40
16
40 < x ≤ 50
2
Complete the cumulative frequency table for the time spent answering
emails.
Time, t
t=0
t ≤ 10
t ≤ 20
t ≤ 30
t ≤ 40
t ≤ 50
minutes
Cumulative
0
frequency
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(2 marks)
©JustMaths 2013
Q4. 90 students took an examination. The grouped frequency table below
shows their results.
Mark (x)
Frequency
0 < x ≤ 10
3
10 < x ≤ 20
10
20 < x ≤ 30
17
30 < x ≤ 40
30
40 < x ≤ 50
21
50 < x ≤ 60
7
60 < x ≤ 70
2
a) On the grid below draw a cumulative frequency graph.
b) Find an estimate for the median mark.
The pass mark for the examination was 28.
c) Find an estimate for the number of students who passed the
examination.
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(6 marks)
©JustMaths 2013
Q5. The cumulative frequency table summarises the time taken by the 95
competitors who completed the men’s 15 km cross-country skiing event
in the Winter Olympics of 2010.
Time (t,
t≤
t≤
t≤
t≤
t≤
t≤
t≤
t≤
t≤
t≤
t≤
t≤
minutes)
33
34
35
36
37
38
39
40
41
42
45
50
0
1
24
48
61
70
75
79
80
85
92
95
Cumulative
frequency
a) How many competitors took more than 36 minutes but no more than 39
minutes?
b) Draw a cumulative frequency diagram to represent this information. The
first five points have been done for you.
c) Use your diagram to find an estimate of:
i.
The median time taken.
ii.
The interquartile range of the times taken.
(6 marks)
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©JustMaths 2013