Moving Averages
Objectives:
D Grade
B Grade
Interpret a Time Series Graph
Construct a Time Series Graph and Plot the
Moving Averages
Moving Averages
A line graph is a series of points joined with straight lines
e.g.
a patient’s temperature was recorded every 2 hours
after receiving medication:
Note the features:
Temperature oC
Temperature over time
Title
Axis Labels
What does this line
represent?
The points are plotted
as coordinates
Normal
body temperature
42
41
40
39
38
37
The points are joined
with straight lines
36
35
0
2
4
6
8
Time after medication (hrs)
10
12
A second set (or more)
of data may be added to
the graph.
Moving Averages
Because the line graph of temperature was plotted against time
it can also be called a ‘Time Series Graph’
Time Series Graphs are often used by people to identify trends over
a period of time where they may be natural fluctuations.
For example, after installing loft and cavity wall insulation a
householder wants to review his gas bills to see if he is saving money.
Moving Averages
A graph of gas bills plotted against time.
Cost of Gas Bill
300
Cost (£)
250
200
150
100
50
0
1st
3rd
2nd
4th
1st
2006
Year / Quarter
3rd
2nd
4th
2007
rd, 4th?
Why is there
so much
fluctuation
in the
a pattern?
the x axis
labelled
with years
andgraph
1st, 2–ndis
, 3there
The
1st quarter
is winterwater,
whenetc.,)
you would
to use
a lot
of gas for
heating,
Utility
(gas, electric,
bills areexpect
sent out
every
3 months
(quarter
of a year)
rd
the 3 quarter is the summer when you don’t use the heating.
Moving Averages
A different number of points for a moving average can be selected
depending upon the data being analysed. Different types of data
suit different moving averages
Which type of moving average which suit which data set?
Electricity Bill
Three-point moving average
Gas Bill
Four-point moving average
Half-term test results
Five-point moving average
Phone Bill
Six-point moving average
Daily Superstore Sales
Seven-point moving average
Termly test results
Moving Averages
Time Series Graph
Year
2006
2007
2nd 3rd
4th
1st
2nd 3rd
2008
Quarter
1st
4th
1st
2nd 3rd
Ice Cream Sales (£)
340 525 965 470 355 510 1100 375 410 555 1150 485
Ice Cream Sales (£)
Plot the data as a time series graph:
This is essentially a line graph. The time is always plotted on the x-axis
1200
x
x
1000
x
800
600
400
x
x
x
x
x
x x
x
x
200
2006
2007
2008
4th
Representing Data
Moving Averages
Moving Averages are a way of looking at a trend over a period of time.
For a four-point the mean is calculated from the first four pieces of data, then the next point is
calculated by moving the selection one place across to calculate the mean of 4 points again
Year
Quarter
2006
2nd 3rd
2007
2nd 3rd
2008
2nd 3rd
Calculate the mean of the
first 4 points
i.e.i.e.
second
4 points
1 Ice Cream Sales (£) 340 525 965 470 355 510 1100 375 410 555 1150 485 525+965+470
340+525+965+470
= 575
+355=
579
Moving Average
575
4
Ice Cream Sales (£)
2
1st
4th
1st
4th
1st
4th
Ice Cream Sales (£) 340 525 965 470 355 510 1100 375 410 555 1150 485
Moving Average
575 579 575 609 585 599 610 623
1200
1000
x
x
x
The moving average point is
plotted in the middle of the 4
points the average is taken
from
800
600
400
x
x
x
x
x
x
x
x
xx
x
x
x
x
x
x
x
For a 3 point moving average
take the mean over 3 points,
for a 5 point moving average
take the mean over 5 points,
etc.
200
2006
2007
You can see there is a general
increase in sales over time
2008
Moving Averages
P20 Q 5
Year
2006 2006 2006 2006
Quarter 1st
2nd
3rd
4th
Cost
£230 £120
£50
£80
Four-point moving
£120 £116
average
2007
1st
£215
2007
2nd
£120
2007
3rd
£25
2007
4th
£55
P21 Q 6
Day
Mon
Mon
Tue
Tue
Wed
Session
a.m.
p.m.
a.m.
p.m.
a.m.
Number
220
210
243
215
254
Two point
215
226.5
229
234.5
moving average
Wed
p.m.
218
Thu
a.m.
251
Thu
p.m.
201
Fri
a.m.
185
Fri
p.m.
152
Moving Averages
P21 Q 7
Year
2005
2006
2006
2006
2007
2007
2007
Session
Autumn Spring Summer Autumn Spring Summer Autumn
Exam Result (%)
86
93
70
83
93
67
77
P21 Q 8
Jul-04
Oct-04 Jan-05 Apr-05
Jul-05
Oct-05 Jan-05 Apr-06
120
x
100 x
Sales (£ thousands)
Quarter
Shop Sales
x
x
80
60
x
40
x
20
x
0
x
Moving Averages
P20 Q 5
Year
2006 2006 2006 2006 2007 2007 2007
Quarter 1st
2nd
3rd
4th
1st
2nd
3rd
Cost
£230 £120
£50
£80
£215 £120
£25
Four-point moving
£120 £116 £116.25 £110 £103.75
average
2007
4th
£55
250
x
x
200
Cost (£)
150
100
x
x
x
x x x
x
50
x
x
x
0
1st
2nd
3rd
4th
1st
2nd 3rd
2006
2007
Time (year, quarter)
4th
The trend is moving downwards which means that the electricity costs are falling
Moving Averages
P21 Q 6
Day
Mon
Mon
Tue
Tue
Wed
Wed
Thu
Thu
Fri
Fri
Session
a.m.
p.m.
a.m.
p.m.
a.m.
p.m.
a.m.
p.m.
a.m.
p.m.
Number
220
210
243
215
254
218
251
201
185
152
Two point
215
226.5
229
234.5 236
234.5 226
193
168.5
moving average
270
x
Number Present
250
x
230
210
190
170
150
x x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
The trend is downwards – starting low on Monday, then rising to Wednesday, but
Falling sharply towards Friday.
Moving Averages
P21 Q 7
100
Year
2005
2006
2006
2006
2007
2007
2007
Session
Autumn Spring Summer Autumn Spring Summer Autumn 90
x
Exam Result (%)
86
93
70
83
93
67
77
80
83
82
82
81
79
x
x
x
x
x
x
x
x
70
x
x
60
P21 Q 8
Quarter
Shop Sales
Jul-04
100
Oct-04 Jan-05 Apr-05
40
10
80
57.5
60
62.5
Jul-05
110
Oct-05 Jan-05 Apr-06
50
12
86
63
64.5
120
x
c. The trend is slightly upwards
67= 50+12+86 +x
4
67 × 4 = 50 + 10 + 86 + x
Sales (£ thousands)
d. The next point would probably lie at 67
100 x
60
40
268 = 146 + x
x = 122
So the next quarter sales would be about £122 000
x
x
80
x
x
x
x
x
x
x
x
20
x
0
x