CS110: Introduction to Computer Science Lab Module 7
Index Numbers: Gasoline and Inflation
Why We Need the Consumer Price Index
When were gas prices their
highest?
Quantitative Concepts and Skills
Percentages
Ratios
Proportions
Relative Change
Graph: XY scatter plot
Prepared for SSAC by
Semra Kilic-Bahi, Colby-Sawyer College, New London NH
Modified by Fred Annexstein
© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2005
1
Background
Index numbers are used to standardize measurements made at different
times or different places so they can be directly compared. This module
focuses on the use and meaning of index numbers. In particular, it examines
the gasoline price index and consumer price index.
The index number is defined as a value relative to a reference value
Index Number 
Value
 100
Reference Value
The reference value is the value, chosen at one particular time or place,
to which values at other times and/or other places will be compared. The
equation assigns an index number of 100 to the reference time or location.
Making comparisons with Index Numbers: The main purpose of index numbers
is to make comparisons. One can compare the prices in one particular year to the
prices in the reference year for a particular product or service.
Comparisons can also be made when neither value is the reference value:
Cost yearA
CostyearB

Index yearA
Index yearB
2
Overview
The Consumer Price Index (CPI) applies to a wide variety of consumer goods and
services. The Bureau of Labor Statistics (BLS) measures two consumer price indices.
The Urban Consumers Price Index (CPI-U) covers all urban consumers, about 80%
of the U.S. population. The Wage Earners Consumer Index (CPI-W) is based on the
purchasing habits of only wage earners. This module will use the CPI-U. Because the
CPI is used as an economic indicator and a means of adjusting dollar values, it affects
many aspects our lives.
The relative change in the CPI from one year to the next is referred as the rate of inflation.
Inflation Rate fromYear 1 to Year 2 
CPI Year2  CPI Year1
CPI Year1
If we want to compare prices fairly we must take inflation into account: we must adjust prices for inflation. To
adjust for inflation, we find the equivalent price in a later year.
Equivalent Price Year2 CPI Year2

Actual Price Year1
CPI Year1
Slide 4 poses the problem: Was gasoline really more expensive in 2005 than it was in 1980?
Slides 5-7 explore the problem by building and using a Gas Price Index.
Slides 8-13 uses the Consumer Price Index to compare the cost of gasoline with the inflation of costs in
general, and Slides 14 and 15 chart the cost of gasoline in 2005 dollars for 1978-2005.
Slides 16-17 give the end-of-module assignments.
3
The Cost of Gasoline
C
Year
Price ($)
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
0.65
0.88
1.22
1.35
1.28
1.23
1.20
1.20
0.93
0.96
0.96
1.06
1.22
1.20
1.19
1.17
1.17
1.21
1.29
1.29
1.12
1.22
1.56
1.53
1.44
1.64
1.92
2.32
Problem: Is gasoline more expensive now (2005)
than it has been in the past?
Recreate this spreadsheet and graph that show the cost of a
gallon of gasoline year by year from 1978 through 2005.
The Price of Gasoline
$2.50
Cost per Gallon
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
B
$2.00
$1.50
$1.00
$0.50
$0.00
1975
1980
1985
1990
1995
2000
2005
Year
Color convention throughout this module
= Cell with a number in it
= Cell with a formula in it
It certainly looks like it,
doesn’t it? But what
about inflation?
4
Resource: Bureau of Labor Stat. http://data.bls.gov/cgi-bin/surveymost?ap. The value for 2005 is estimated.
Exploring the Question: Making a Gasoline Price Index
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
C
D
We can construct a Gasoline Price Index (GPI)
using 1978 as a reference. Add a column to the
spreadsheet and calculate the Gasoline Price
Index for each year since 1978.
Gasoline Price
Index (ref
year: 1978)
Price ($)
0.65
0.88
1.22
1.35
1.28
1.23
1.20
1.20
0.93
0.96
0.96
1.06
1.22
1.20
1.19
1.17
1.17
1.21
1.29
1.29
1.12
1.22
1.56
1.53
1.44
1.64
1.92
2.32
100.00
135.38
187.69
207.69
196.92
189.23
184.62
184.62
143.08
147.69
147.69
163.08
187.69
184.62
183.08
180.00
180.00
186.15
198.46
198.46
172.31
187.69
240.00
235.38
221.54
252.31
295.38
356.92
=(C4/$C$4)*100
Compare these cell formulas to the
formula for an index number on Slide 2.
=(C12/$C$4)*100
Because we want all of the formulas to point back to the value for 1978, we use an
absolute cell reference (the dollar signs). For more information on absolute and
relative cell references in EXCEL, see “cell reference” in the EXCEL help file.
Gasoline Price Index (Ref 1978)
Price Relative to 1978
B
400
300
200
100
0
1975
1980
1985
1990
1995
2000
2005
The graph of
the GPI is the
same shape as
the graph of
the cost of
gasoline on
Slide 4. Why?
Year
In 2005, the price of gasoline was
357% of the price of gasoline in 1978 –
an increase of more than 2.5 times!
5
Using the GPI to Make Comparisons
Suppose it cost $12 dollars to fill a gas tank in 1980. How much would
it have cost to fill the same tank in 2005?
We can answer the question by using the GPI (Gasoline Price Index) that we developed in
Slide 5. First we divide the GPI for year 2005 by the GPI for 1980 to find a comparison
factor (it will be a multiplier) that will express the cost of gasoline in 2005 relative to the cost
of gasoline in 1980:.
GPI 2005 356.92

 1.91
GPI1980 187.27
Thus the 2005 price is almost twice the 1980 price.
Next you multiply what you would have paid for gas in 1980 by the comparison factor
to find what you would have paid in 2005.
Gas 2005  Gas1980
GPI 2005
 $12 1.91
GPI1980
Thus, if you had filled your gas tank for $12 in 1980, you would have paid $12.00 × 1.91 =
$22.92 to fill your gas tank in 2005
Be prepared to discuss this calculation using the words ratio and proportion
6
Making More Comparisons
B
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
C
D
E
Equivalent
Gasoline Price of a $12
Index (ref tank of gas
year: 1978) in 1980 ($)
Price ($)
0.65
0.88
1.22
1.35
1.28
1.23
1.20
1.20
0.93
0.96
0.96
1.06
1.22
1.20
1.19
1.17
1.17
1.21
1.29
1.29
1.12
1.22
1.56
1.53
1.44
1.64
1.92
2.32
100.00
135.38
187.69
207.69
196.92
189.23
184.62
184.62
143.08
147.69
147.69
163.08
187.69
184.62
183.08
180.00
180.00
186.15
198.46
198.46
172.31
187.69
240.00
235.38
221.54
252.31
295.38
356.92
6.39
8.66
12.00
13.28
12.59
12.10
11.80
11.80
9.15
9.44
9.44
10.43
12.00
11.80
11.70
11.51
11.51
11.90
12.69
12.69
11.02
12.00
15.34
15.05
14.16
16.13
18.89
22.82
If we can answer the question for 2005, we can
answer it too for any year that we know the GPI.
So, if it cost $12 dollars to fill a gas tank in 1980,
how much would it have cost to fill the same
tank for each year from 1978 to 2005?
Add another column in the
spreadsheet to show the price
for each year.
We are not showing a graph of the $12
tank of gas vs. time, because it would
be yet another rescaled version of the
graph of GPI. But now we can come to
the point: How would these graphs of
gasoline prices differ from graphs of
consumer prices in general over those
years? What about inflation?
 12 
GPI 2005
GPI 1980
Compare this cell formula to the formula
for the price of gas in 2005 on slide 6.
7
Consumer Price Index
C
Annual CPI-U
65.2
72.6
82.4
90.9
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124.0
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163.0
166.6
172.2
177.1
179.9
184.0
188.9
194.9
We have observed that the price of gasoline has increased
over time. But the price of consumer goods in general may
have increased even more. If so, the cost of gas in 2005
might actually cost less relative to everything else in 2005
than it did earlier. The way to find out is to look at the
Consumer Price Index.
15
Click on the object to create this
spreadsheet. Now graph the
Consumer Price Index vs. Time.
Certainly there
has been an
inexorable rise in
prices in general
from 1978 to
2005. How do the
across-the-board
prices in 2005
compare
specifically to
those in 1980?
10
Consumer Price Index
200
5
150
CPI
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
B
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
100
50
0
-995
5
1005
2005
0
1975
1980
1985
1990
1995
2000
2005
Year
8
Using the CPI to Make Comparisons
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
B
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
C
Annual CPI-U
65.2
72.6
82.4
90.9
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124.0
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163.0
166.6
172.2
177.1
179.9
184.0
188.9
194.9
We wish to compare the cost of goods and services in
1980 to the cost of goods and services in 2005. According
to these tabulated values of the CPI-U, what would have
cost $82.40 in 1980 would have cost $194.90 in 2005.
15
In general, costs in 2005
were how many times the
costs in 1980?
CPI 2005 194.9

 2.36
CPI1980 82.4
10
Recall (Slide 4) a gallon of gas cost $1.22 in 1980. In
general, things that cost $1.22 in 1980 (“in 1980
dollars”) cost $1.22 × 2.36 = $2.89 in 2005 (“in “2005
dollars”). But a gallon of gas cost $2.32 in 2005. So
gasoline was not relatively more expensive in 2005
than it was in 1980.
5
0
-995
5
1005
2005
We can have Excel make this kind of comparison for
every year since 1980 from our data on CPI and GPI.
9
Comparing the GPI and the CPI
B
Add the four columns
of cell equations to
recreate this
spreadsheet.
Columns E and F are
the indexes relative
to the 1980 value.
Columns G and H
are the percentage
increases of the
indexes since 1980.
For comments on this
table, see next slide.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
C
Annual CPI-U
65.2
72.6
82.4
90.9
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124.0
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163.0
166.6
172.2
177.1
179.9
184.0
188.9
194.9
D
E
F
G
Gasoline
Price Index
CPI
(ref year: CPI(Year) / GPI(Year) / Increase
1978)
CPI(1980) GPI(1980)
(%)
100.00
135.38
187.69
1.00
1.00
0%
207.69
1.10
1.11
10%
196.92
1.17
1.05
17%
189.23
1.21
1.01
21%
184.62
1.26
0.98
26%
184.62
1.31
0.98
31%
143.08
1.33
0.76
33%
147.69
1.38
0.79
38%
147.69
1.44
0.79
44%
163.08
1.50
0.87
50%
187.69
1.59
1.00
59%
184.62
1.65
0.98
65%
183.08
1.70
0.98
70%
180.00
1.75
0.96
75%
180.00
1.80
0.96
80%
186.15
1.85
0.99
85%
198.46
1.90
1.06
90%
198.46
1.95
1.06
95%
172.31
1.98
0.92
98%
187.69
2.02
1.00
102%
240.00
2.09
1.28
109%
235.38
2.15
1.25
115%
221.54
2.18
1.18
118%
252.31
2.23
1.34
123%
295.38
2.29
1.57
129%
356.92
2.37
1.90
137%
15
10
5
0
-995
5
1005
2005
H
GPI
Increase
(%)
0%
11%
5%
1%
-2%
-2%
-24%
-21%
-21%
-13%
0%
-2%
-2%
-4%
-4%
-1%
6%
6%
-8%
0%
28%
25%
18%
34%
10
57%
90%
Comparing the changing GPI to inflation: Table
B
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
C
Annual CPI-U
65.2
72.6
82.4
90.9
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124.0
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163.0
166.6
172.2
177.1
179.9
184.0
188.9
194.9
D
E
F
G
Gasoline
Price Index
CPI
(ref year: CPI(Year) / GPI(Year) / Increase
1978)
CPI(1980) GPI(1980)
(%)
100.00
135.38
187.69
1.00
1.00
0%
207.69
1.10
1.11
10%
196.92
1.17
1.05
17%
189.23
1.21
1.01
21%
184.62
1.26
0.98
26%
184.62
1.31
0.98
31%
143.08
1.33
0.76
33%
147.69
1.38
0.79
38%
147.69
1.44
0.79
44%
163.08
1.50
0.87
50%
187.69
1.59
1.00
59%
184.62
1.65
0.98
65%
183.08
1.70
0.98
70%
180.00
1.75
0.96
75%
180.00
1.80
0.96
80%
186.15
1.85
0.99
85%
198.46
1.90
1.06
90%
198.46
1.95
1.06
95%
172.31
1.98
0.92
98%
187.69
2.02
1.00
102%
240.00
2.09
1.28
109%
235.38
2.15
1.25
115%
221.54
2.18
1.18
118%
252.31
2.23
1.34
123%
295.38
2.29
1.57
129%
356.92
2.37
1.90
137%
15
10
5
0
-995
5
1005
2005
H
GPI
Increase
(%)
0%
11%
5%
1%
-2%
-2%
-24%
-21%
-21%
-13%
0%
-2%
-2%
-4%
-4%
-1%
6%
6%
-8%
0%
28%
25%
18%
34%
57%
90%
This says costs in 1989
were 1.5x the costs in
1980.
This says there was
50% inflation between
1980 and 1989.
This says gas actually
decreased 13% over the
same period.
Now graph Columns E
and F vs. year to see
the change in CPI and
GPI relative to their
values in 1980.
11
Comparing the changing GPI to inflation: Graph
GPI compared to CPI
CPI relative to CPI(1980)
GPI relative to GPI(1980)
Index relative to 1980 value
2.50
2.00
Over the 1980-2005 period, gas
prices started out tracking the
CPI, but then they fell far behind
as the CPI rose but the GPI did
not – until recently, that is, when
the GPI has been rising faster
than the CPI.
1.50
1.00
0.50
0.00
1980
1985
1990
1995
Year
2000
2005
This graph of the rising CPI shows the
amount of inflation since 1980. When
speaking of “graphs of inflation,”
however, one generally is referring to
the annual inflation (“inflation rates”).
Inflations rates are different – they are
the relative change over a one-year
period (for example, a 10% change over
a 10-year period is vastly different than
a 10% change over a one-year period).
To draw a graph of the annual inflation
rate from 1980 to 2005, we need to go
back to the data of Slide 8.
12
Inflation Rate
C
Annual CPI-U
65.2
72.6
82.4
90.9
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124.0
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163.0
166.6
172.2
177.1
179.9
184.0
188.9
194.9
D
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
E
Inflation Rate
%
11.35
13.50
10.32
6.16
3.21
4.32
3.56
1.86
3.65
4.14
4.82
5.40
4.21
3.01
2.99
2.56
2.83
2.95
2.29
1.56
2.21
3.36
2.85
1.58
2.28
2.66
3.18
Retrieve your data from the
spreadsheet of Slide 8, add two
columns of cell equations to track
the year-to-year inflation rate, and
graph inflation rate vs. time.
Note: the CPI of 1979 (72.6) is 11.35%
higher than the CPI of 1978 (65.2), so
we are saying that the inflation rate
during 1978 was 11.35%.
15
Inflation Rate (%)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
B
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
10
5
0
1975
1980
1985
1990
1995
2000
2005
Year
13
Adjusting Gasoline Prices for Inflation
B
We can make the comparison a different way.
We can ask how much a gallon of gasoline back
then “was worth” in the dollars of 2005.
For example, in 2005 you would have had to pay
194.9/82.4 = 2.37 times what you would have
paid for the same goods in 1980. So the $1.22
you would have paid for a gallon of gas in 1980
would buy 2.37×$1.22 = $2.89 worth of goods in
2005 (whereas gas cost “only” $2.32 a gallon).
Retrieve your data for the CPI (Slide
8) and the Price of a Gallon of Gas
(Slide 5), and add a column of cell
equations to calculate how much a
gallon of gas was worth year by year
in 2005 dollars.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
C
Annual CPI-U
65.2
72.6
82.4
90.9
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124.0
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163.0
166.6
172.2
177.1
179.9
184.0
188.9
194.9
F
G
Adjusted
Gas Price Gas Price
($)
(2005$)
0.65
1.94
0.88
2.36
1.22
2.89
1.35
2.89
1.28
2.59
1.23
2.41
1.20
2.25
1.20
2.17
0.93
1.65
0.96
1.65
0.96
1.58
1.06
1.67
1.22
1.82
1.20
1.72
1.19
1.65
1.17
1.58
1.17
1.54
1.21
1.55
1.29
1.60
1.29
1.57
1.12
1.34
1.22
1.43
1.56
1.77
1.53
1.68
1.44
1.56
1.64
1.74
1.92
1.98
2.32
2.32
Now graph the gas price and the
14
adjusted gas price vs. time 
Adjusting Gasoline Prices for Inflation
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
C
Annual CPI-U
65.2
72.6
82.4
90.9
96.5
99.6
103.9
107.6
109.6
113.6
118.3
124.0
130.7
136.2
140.3
144.5
148.2
152.4
156.9
160.5
163.0
166.6
172.2
177.1
179.9
184.0
188.9
194.9
F
G
Adjusted
Gas Price Gas Price
($)
(2005$)
0.65
1.94
0.88
2.36
1.22
2.89
1.35
2.89
1.28
2.59
1.23
2.41
1.20
2.25
1.20
2.17
0.93
1.65
0.96
1.65
0.96
1.58
1.06
1.67
1.22
1.82
1.20
1.72
1.19
1.65
1.17
1.58
1.17
1.54
1.21
1.55
1.29
1.60
1.29
1.57
1.12
1.34
1.22
1.43
1.56
1.77
1.53
1.68
1.44
1.56
1.64
1.74
1.92
1.98
2.32
2.32
Here is the answer to our question. The graph
shows the cost of a gallon of gasoline in 2005
dollars from 1978 through 2005. Gas was more
expensive in 1979-1982 than in was in 2005
according to these data.
Gasoline in dollars of the time
Cost ofGallon of Gas ($)
B
Gasoline in 2005 dollars
3.00
2.50
2.00
1.50
1.00
0.50
0.00
1975
1980
1985
1990
1995
2000
2005
2010
Year
15
End of Module Assignments
0. Expand your tables so that you can compare trends in gasoline prices to that of
crude oil (see the Excel object at right).. You should obtain a graph, extending slide 12
to include a COI (crude oil index (ref 1980)) trend line. Explain what you observe.
1. Expand the table in Slide 5 to give the gasoline price index over the period 1978 to
present (use $2.20 for 2006 and $2.79 for 2007). Also, use 1988 as the reference year.
Multiplot the GPI and COI with the 1988 reference year with the GPI and COI with the
1978 reference year (Slide 5). What do you observe? How do the graphs differ?
Explain what you observe.
2. Redo the calculations in Slide7 to find the equivalent of gasoline which cost $12 in
1980 for each year over the period 1978 to present using 1988 as the reference year
and compare it to the results from using 1978 as a reference year. What do you
observe? Does the result make sense? Explain!
3. Expand the table in Slide 8 and create a scatter plot of the CPI from 1913 to present
(See ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt)
4. Redo the calculations in Slide 15 by evaluating the equivalent price of an item which
cost $1 in 1988 for each year since 1913. In what year was the purchasing power of
1988’s $1 the highest?
5. Use your table from assignment 3 to calculate and graph (scatter plot) the rate of
inflation since 1946. What do you observe? Write a paragraph discussing the behavior 16
of the rate of inflation in terms of major national and world events during this period.
End of Module Assignments
Extra Credit: Use the website http://www.sca.isr.umich.edu/ to
discover trends in indexes used to track consumer opinions. Create a
graph that compares at least two trends. Explain your results.
References
Using and Understanding Mathematics: A Quantitative Approach, by Jeffrey Bennett and William
Briggs
Contemporary College Algebra, by Don Small
For All Practical Purposes, Mathematical Literacy in Today’s World, by COMAP
Bureau of Labor Statistics Website http://data.bls.gov/
Gas station picture:
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=7113368463&category=834
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