Transcript 2.4 Index Numbers

Statistical Reasoning
for everyday life
Intro to Probability and
Statistics
Mr. Spering – Room 113
2.4 Index Numbers
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
Inflation – an increase in credit relative to available goods
resulting in substantial and continual rise in prices.
Index Number – simple way to compare measurements made at
different times or in different places. The value at one particular
time (or place) must be chosen as the reference value (or base
value). The index number for any other time (or place) is:
index number =
value
100
reference value
--Everything in this journey of life depends on your reference point.--
2.4 Index Numbers
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Example:
COMPARING GASOLINE PRICES ( PER
GALLON)
year
price
Price as a
% of 1975
Price Index
(1975=100)
1955
1965
1975
1985
1995
$ 0.291
$ 0.312
$ 0.567
$ 1.196
$ 1.205
51.3%
55.0%
100.0%
210.9%
212.5%
51.3
55.0
100
210.9
212.5
2.4 Index Numbers
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CONSUMER PRICE INDEX (CPI) – computed and
reported monthly, represents an average of prices in a
sample of more than 60,000 goods, services, and
housing costs
http://www.bls.gov/cpi/
http://data.bls.gov/cgi-bin/surveymost?cu
2.4 Index Numbers
GOOD LUCK!!!!
2.4 Index Numbers
Suppose the cost of gasoline today is $ 2.60 per gallon. What is
the price index number for gasoline today, with 1975 price
($ 0.567) as the reference value?
2.60
 4.58553 100%  458.55%  458.55
0.567
Suppose that it cost $10 to fill your gas tank in 1975. How much
will it cost now?
$10.00(4.5855)  $45.86
2.4 Index Numbers
Suppose it would have cost you $15 to fill your
gas tank in 1985 (index # 210.9). How
much will it cost you now?
index now 458.55

 2.17  217%
index 1985 210.9
cost now  2.17($15)  $32.55
2.4 Index Numbers
The average cost of tuition, fees, and room and board at a four-year public
universities rose from $2,490 in 1980 to $7,800 in 1997. Calculate the
percentage rise in cost from 1980 to 1997, and compare it to the overall rate
of inflation as measured by the CPI.
%Change 
CPI change 
(7800  2490)
100%  213.3% increase
2490
index #1997  index #1980 160.5  82.4

100%  95% increase
index #1980
82.4
***Therefore, the tuition rate increased more than twice as much as the
inflation rate for the same time period.
2.4 Index Numbers
 Remember:
----Failing to prepare is preparing to fail------GIVING your best EFFORT based on the KNOWLEDGE you
have attained is not GOOD enough if the amount of
KNOWLEDGE you possess reflects a LACK of effort to
LEARN--- Lawrence W. Schott