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3D Index Numbers - Index Numbers The CPI Friday(continued...

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Index Numbers: The CPI Friday January 14, 2011 (continued) What is an Index Number? An index number provides a simple way to compare measurements made at different times or in different places. The value at one particular time (or place) must be chosedn as the reference value. The index number for any other times (or place) is index number = value reference value × 100 (1) Wednesday January 1, 2011 Example 1. Consider the average gas prices by year as given below: Year Price (in cents) Price as a percentage of 1975 price Price index (1975 = 100) 1955 29.1 51.3% 51.3 1965 31.2 55.0% 55.0 1975 56.7 100.0% 100.0 1985 119.6 210.9% 210.9 1995 120.5 212.5% 212.5 2005 231.0 407.4% 407.4 Here we have chosen the 1975 price to be the reference value (i.e. all other prices are compared to the 1975 price in the last two columns). The percentages and indices were computed using (1) as follows: 1955price 1975price = 29 . 1cents 56 . 7cents = 0 . 513 = 51 . 3% Therefore the index number for the 1955 gas price using the 1975 gas price as the reference value is 51.3. The indices for the gas prices in other years is computed similarly. 1
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1. Making Comparisons with Index numbers Main purpose for index numbers is to facilitate comparisons. Example 2. Using the table above we can easily compare gas prices in various years to the gas price in 1975. For example, the index for 1995 is 121.5. This means that the price of gas in 1995 was 212.5% of the price of gas in 1975. Equivalently, the 1995 price was 2.12 times the 1975 price. Example 3. Using the above table for gas prices, we can also compare two gas prices when neither of the two prices is the reference price. Suppose we want to know how
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