The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Name:
Innovation & excellence
HW1
HW1 –– Grade
Grade E/F/G
C
Finding an Estimate of the Mean
1.
Teacher
Assessment
A police officer records the speeds of 60 cars on a dual carriageway.
Speed (mph)
(a)
Frequency
40 to less than 50
9
50 to less than 60
27
60 to less than 70
21
70 to less than 80
3
Midpoint
Write down the modal class.
Answer .................................................................. mph
(1)
(b)
Use the class midpoints to calculate an estimate of the mean speed of these cars.
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......................................................................................................................................
Answer .................................................................. mph
(3)
(Total 4 marks)
2.
Jane records the times taken by 30 pupils to complete a number puzzle.
Time, t (minutes)
Number of pupils
2<t4
3
4<t6
6
6<t8
7
8 < t  10
8
10 < t  12
5
12 < t  14
1
Calculate an estimate of the mean time taken to complete the puzzle.
................................................................................................................................................
................................................................................................................................................
Answer ..................................... minutes
(4)
The Robert Smyth School
1
The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
3.
Chloe records the number of goals scored by her favourite football team in each of 40 matches.
Number of goals
Frequency
0
7
1
15
2
13
3
2
4
2
5
1
(a)
Chloe’s father watched one of these matches on TV.
What is the probability that the team scored at least one goal in that match?
.....................................................................................................................................
(b)
Answer .........................................................................
Calculate the mean number of goals scored per match.
(2)
.....................................................................................................................................
Answer .........................................................................
(3) (Total 5 marks)
4.
The table shows the age, in years, of workers in a factory.
Age, x (years)
Number of workers
15  x < 20
4
20  x < 25
10
25  x < 30
6
30  x < 40
22
40  x < 60
8
Calculate an estimate of the mean age of these workers.
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...............................................................................................................................................
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Answer ....................................................... years
(Total 4 marks)
Success:
The Robert Smyth School
Target:
2
The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
HW2 – Grade B
Calculating and Plotting Moving Averages
1.
Teacher
Assessment
The table shows the percentage of men in Britain who smoked.
The data was recorded every two years from 1974 to 1988.
(a)
Year
1974
1976
1978
1980
1982
1984
1986
1988
%
50
46
45
42
38
36
35
33
Calculate the first value of the three-point moving average for these data.
.....................................................................................................................................
.....................................................................................................................................
Answer ........................................................
(2)
(b)
The graph shows the three-point moving average for the percentage of men who
smoked, plotted every two years, from 1978.
45
40
Moving
average
35
(%)
30
25
20
1978
1982
1986
1990 1994
Year
1998
2002
2006
The government has set a target of reducing the percentage of male smokers to below
25% by the year 2006.
Comment on whether they will achieve this target.
Justify your answer.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
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3
The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
(c)
The government decides to carry out a survey of male smoking habits.
Give two factors that need to be taken into consideration when planning the survey.
Factor 1 ......................................................................................................................
....................................................................................................................................
Factor 2 ......................................................................................................................
.....................................................................................................................................
(2)
(Total 6 marks)
2.
A coach company recorded the number of bookings it took each quarter over a two-year period.
The figure for the first quarter of 2004 has been missed out.
2003
(a)
2004
Quarter
1st
2nd
3rd
4th
Number of bookings
24
52
83
37
1st
2nd
3rd
4th
61
86
40
Explain why a four-point moving average is appropriate for this data.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(1)
(b)
Show that the first value of the four-point moving averages is 49.
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Answer ...............................................................
(1)
(c)
The second value of the four-point moving averages is 51.
Calculate the number of bookings taken in the first quarter of 2004.
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.....................................................................................................................................
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Answer ...............................................................
(3)
(Total 5 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
3.
The table shows the amount of water, in m3, used every six months by a family over a period of three years.
Date
April
2002
Oct
2002
April
2003
Oct
2003
April
2004
Oct
2004
36
58
38
60
42
64
Water
used (m3)
47
Two-point
moving average
(a)
The first two-point moving average is 47 m3
Calculate the other two-point moving averages.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
The time series graph shows the original data.
Plot all the moving averages.
65
×
×
60
×
55
50
Water
used (m 3 ) 45
×
40
×
35
×
30
0
April
2002
Oct
2002
April
2003
Oct
2003
April
2004
Oct
2004
Date
(2)
(c)
Describe the trend shown by the moving averages.
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 5 marks)
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5
The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
4.
The table shows the cost of the gas at the end of every three months and some four-point moving
averages.
2002
2003
2004
Year
Quarter
1st
2nd
3rd
4th
1st
2nd
3rd
4th
1st
2nd
3rd
Cost (£)
86
90
93
99
94
94
97
103
94
98
101
Four-point
moving average
92
94
95
96
97
97
98
4th
99
The graph shows the actual cost of the gas and some of the moving averages.
105
100
×
Cost (£)
×
×
×
95
×
×
90
85
2002
2003
Year
Key:
Actual cost
×
(a)
2004
Moving average
On the graph plot the last two four-point moving averages.
(2)
(b)
Use the trend of the moving averages to predict the cost of the gas at the end of the 4th
quarter of 2004.
………...…............……..............................…………….....………….......................
………...…............……..............................…………….....………….......................
………...…............……..............................…………….....………….......................
Answer £ …………………………………
(3)
(Total 5 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
5.
The table shows the number of people enrolled in keep fit classes at a college each term.
2002
Number of people
(a)
2003
Term 1
Term 2
Term 3
Term 1
Term 2
22
49
31
28
58
Term 3
The first three-point moving average is 34.
(i)
Calculate the second three-point moving average.
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............................................................................................................................
Answer .........................................................................
(2)
(ii)
Calculate the third three-point moving average.
............................................................................................................................
............................................................................................................................
............................................................................................................................
Answer .........................................................................
(1)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
(b)
The time series graph shows the original data.
Plot all the moving averages on the graph.
70
60
Number
of people
50
40
30
20
0
Term 1
2002
Term 2
2002
Term 3
2002
Term 1
2003
Term 2
2003
(2)
(c)
Use the trend to estimate the number of people enrolled in keep fit classes at the college in
Term 3 of 2003.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer .........................................................................
(3) (Total 8 marks)
Success:
The Robert Smyth School
Target:
8
The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
HW3 – Grade A/A*
Problem solving using frequency tables
1.
(a)
Teacher
Assessment
A road safety officer records the speed of 50 cars outside a school.
Speed, s (mph)
Frequency
Midpoint
20  s < 25
12
22.5
25  s < 30
27
30  s < 35
8
35  s < 40
3
Use the class midpoints to calculate an estimate of the mean speed of these 50 cars.
......................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer .....................................................mph
(3)
(b)
The table shows the number of accidents outside the school in the last six years.
Year
2000
2001
2002
2003
2004
2005
Number of
accidents
4
5
9
10
9
11
The first 3-point moving average is 6.
Calculate the second and third 3-point moving averages.
....................................................................................................................................
....................................................................................................................................
Answer.........................................and............................................
(3)
(Total 6 marks)
2.
The time taken, in minutes, for a group of students to complete their homework is summarised in
the grouped frequency table.
Time, t (minutes)
Frequency
5 ≤ t < 15
3
15 ≤ t < 25
f
25 ≤ t < 35
7
35 ≤ t < 45
6
45 ≤ t < 55
4
The Robert Smyth School
9
The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
The grouped data was used to calculate an estimate of the mean.
This was found to be 30 minutes.
Calculate the value of the missing frequency, f.
You must show your working.
...............................................................................................................................................
...............................................................................................................................................
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...............................................................................................................................................
...............................................................................................................................................
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Answer ..........................................................................
(Total 4 marks)
3.
The table shows the weights of 100 children in year 7.
An estimate of the mean weight of the children is calculated as 44 kg.
Calculate the values of a and b.
Weight, w (kg)
Frequency
20 < w  30
12
30 < w  40
21
40 < w  50
38
50 < w  60
a
60 < w  70
b
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer a =..............................., b = ……………………..
(Total 6 marks)
The Robert Smyth School
10
The Robert Smyth School
Mathematics Faculty
Module 1
(2b) Analysing & Processing
Innovation & excellence
4.
120 men took part in a fitness test.
The times taken to complete the test are shown in the table.
Time, t (minutes)
(a)
10 < t  12
Frequency
21
12 < t  14
49
14 < t  16
37
16 < t  18
Total
13
120
Which class interval contains the median time taken by these men to complete the test?
You must show your working.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer …………………… < t  …………………………… (2)
(b)
Calculate an estimate of the mean time taken by these 120 men to complete the test.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer ………………………………......... minutes
(c)
(4)
90 women also took part in this fitness test.
An estimate of the mean time taken by these 90 women was calculated.
It was found to be 15.8 minutes.
Calculate an estimate of the mean time taken by all the 210 people to complete this test.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer ………………………………......... minutes
(3) (Total 9 marks)
Success:
The Robert Smyth School
Target:
11