1.
The table shows the number of students at a tutorial college each term since Autumn 2002. The
table also shows the 3-point moving averages for this data except for Spring 2003 and Summer
2005.
Autumn Spring Summer Autumn Spring Summer Autumn Spring Summer Autumn
2002 2003 2003
2003 2004 2004
2004 2005 2005
2005
Number
of
students
48
3-point
moving
average
(a)
30
81
54
39
93
69
57
55
58
62
67
73
80
114
Calculate the 3-point moving average for Spring 2003.
You must show your working.
.....................................................................................................................................
.....................................................................................................................................
Answer ……………………………………………
(2)
(b)
(i)
By continuing the number sequence for the moving averages, predict the 3-point
moving average for Summer 2005.
...........................................................................................................................
...........................................................................................................................
Answer ……………………………………………
(1)
(ii)
Show how the college predicted that the number of students in Autumn 2005
would be 93.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(Total 4 marks)
2.
The table shows the amounts of Jenny’s gas bills from September 2001 to December 2002.
Date
September
2001
December
2001
March
2002
June
2002
September
2002
December
2002
Amount of bill (£)
28.70
32.40
29.10
7.80
30.30
38.60
The Robert Smyth School
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(a)
Explain why a four-point moving average is appropriate for these data.
......................................................................................................................................
......................................................................................................................................
(1)
(b)
Show that the first value of the four-point moving average is £24.50
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
(2)
(c)
Calculate the second value of the four-point moving average for these data.
......................................................................................................................................
......................................................................................................................................
Answer £ .......................................
(2)
(Total 5 marks)
3.
A college records the number of people who sign up for adult education classes each term.
The table shows the numbers from Autumn 2000 to Summer 2002.
Term
Autumn
2000
Spring
2001
Summer
2001
Autumn
2001
Spring
2002
Summer
2002
Number of people
520
300
380
640
540
500
(a)
Calculate the first value of the three-point moving average for these data.
.....................…………………………………………………………………………
Answer ................................................
(2)
(b)
Explain why a three-point moving average is appropriate.
.....................…………………………………………………………………………
.....................…………………………………………………………………………
(1)
The Robert Smyth School
2
The time series graph shows the original data.
The remaining values of the three-point moving average are also plotted (as crosses).
700
600
×
Number
of people
500
×
×
400
300
0
Autumn
2000
Spring
2001
Summer
2001
Autumn
2001
Spring
2002
Summer
2002
Term
(c)
Plot the value from part (a) on the graph.
(1)
(d)
Use the trend to estimate the three-point moving average that would be plotted
at Summer 2002.
Answer ................................................
(1)
(e)
Use the value from part (d) to calculate a prediction of the number of people who will sign
up for adult education classes in Autumn 2002.
.....................…………………………………………………………………………
.....................…………………………………………………………………………
Answer ................................................
(2)
(Total 7 marks)
The Robert Smyth School
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4.
The table shows the costs of the heating bills for a house.
Date of
bill
March
2002
June
2002
Sept
2002
Dec
2002
March
2003
June
2003
Sept
2003
Cost (£)
72
40
28
60
92
56
40
50
Four-point moving average (£)
(a)
You are given that the first four-point moving average is £50. Calculate all the other
four-point moving averages.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
(b)
The time series graph shows the original data.
The first four-point moving average, £50, has also been plotted.
Plot all the other moving averages.
100
80
60
×
Cost (£)
40
20
0
March
2002
June
2002
Sept
2002
Dec
2002
March
2003
June
2003
Sept
2003
Dec
2003
Date of bill
(2)
The Robert Smyth School
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(c)
Draw a trend line and use it to estimate the cost of the December 2003 heating bill. You
must show your working.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer .........................................................................
(3)
(Total 9 marks)
5.
(a)
(48 + 30 + 81)  3
159/3
M1
53
A1
53 with incorrect working or no marking no marks
(b)
(i)
88
B1
Answer in table unless contradicted on answer line
(ii)
(93 + 114 + 57)/3 = 88
3 × their 88 – (114 + 57)
B1
[4]
6.
(a)
Four bills each year, bills every 3 months
Accept: Month repeats every four bills
Do not accept: There are four months
B1
(b)
28.70 + 32.40 + 29.10 + 7.80
M1
98.00 ÷ 4
or
28.70 + 32.40 + 29.10 + 7.80 ÷ 4
98 ÷ 4 on its own SC1
Must see calculation (24.50 is given in question)
A1
(c)
(32.40 + 29.10 + 7.80 + 30.30) ÷4
Alternative: Sept 02 = £1.60 more than Sept 01
Hence average increased by 40p
M1
= £24.90
A1
£24.91 implies M1A0
[5]
7.
(a)
(520 + 300 + 380) ÷ 3
= 400
M1
A1
(b)
Three terms in a year
B1
The Robert Smyth School
5
(c)
Plot their (a) at Spr 2001
1 mm tolerance
(d)
620
B1 ft
B1
600 to 640 inclusive
ft their drawn trend  10 people inclusive
(e)
(620 × 3) – 500 – 540
or (their (d) × 3) – 500 – 540
M1
or Alternate method
Aut 2000 520 – 340(trend) = 180
Aut 2001 640 – 520(trend) = 130
Total (310) ÷ 2 = 155
685(trend) + 155
=840
820
A1 ft
[7]
8.
(a)
(40  28  60  92)
4
Or
(28  60  92  56)
4
Or
(60  92  56  40)
4
55, 59, 62
(b)
(c)
Plotting at correct mid-points
At least 2 points
M1
A1 A1 A1
M1
All 3 of their “correct” plots at mid-points
ft numbers in boxes in (b)
Or correct
A1 ft
A suitable trend line through their points
At least as long as “50-62”
B1 ft
(92  56  40  x)
= 66
4
(trend at mid-point of June 03 & Sept 03)
Trend line doesn’t have to be extended - a value of “64-70”
would be accepted without a line.
Alt: seasonal component Dec = £4
Extrapolate trend line to
Dec 03 = £73
73 + 4
Solving x = £76
£77 from correct method seen
M1
A1 ft
[9]
The Robert Smyth School
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