Cast your mind back to why proportions and percentages were introduced in Section 2. It was because using actual price changes is unsatisfactory in comparing how the prices of different items have altered over time when their basic prices are very different. For example, if the price of a new motor car has gone up by £100 and the price of a new bicycle has gone up by £50 over the same period, which is the more significant price rise? Expressed as a percentage (or price ratio) of its basic price, the bicycle price increase is much the greater of the two and any sensible comparison of the two price increases must take that into account. In other words, comparisons must be based on relative, not absolute, differences.
Absolute price changes are differences in price found by subtraction (new price — old price).
Relative price changes involve dividing by the old price, for example to express the price change as a proportion or percentage of the old price, or to use a price ratio.
In the next section, you will read about the Consumer Price Index and Retail Prices Index; these are price indices used to measure overall price changes in the UK.
Measures based on relative comparisons have been introduced already, namely proportional or percentage price increases and price ratios. The audio session which follows introduces a third measure called a price index. A price index shows how the price of a single item, or a basket of goods, is related to the price at a particular chosen time (the base year).
The word ‘index? has a number of different but connected meanings. An index appears at the back of a book to help you find what is in it. The index finger (next to the thumb) is for pointing things out. The plural of the word ‘index?, used mathematically, is ‘indices? (just as the plural of vertex, a corner of a geometric figure made of straight lines, is vertices). There is a link with words such as ‘indicative? and ‘indicator?.
In mathematics, you may also have come across the word ‘index? used as another name for the exponent or power to which a number is raised. (This use is not related directly to price indices.)
Listen to the audio clip below, called ‘Constructing a price index?. You will need your calculator, pen and paper as you work through the band.
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