- Current section: Introduction
- Learning outcomes
- 1. Politicians and journalists
- 1.1: Introduction
- 1.2: Are we getting better off?
- 1.3: A statistical interlude—averages
- 1.4: Price ratios and price indices
- 1.5: The UK Government price indices
- 1.6: Using the price indices
- 1.7: Some mathematical themes
- 1.8: Summary
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This unit looks at a wide variety of ways of comparing prices and the construction of a...
This unit looks at a wide variety of ways of comparing prices and the construction of a price index. You will also look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You wil also look at the important statistical and mathematical ideas that contribute to the construction of a price index.
After studying this Unit you should be able to:
- calculate the mean, weighted mean and the median of a batch of numbers;
- calculate a percentage and a percentage price increase;
- use a weighted mean to find an average percentage price increase (given the weights);
- use the statistical facilities of your calculator to find the mean, the median and (given the weights) the weighted mean of a batch of numbers;
- calculate a percentage price increase and a price ratio from a price index;
- use price ratios to calculate values of a price index;
- calculate the RPI and the CPI given the relevant information;
- describe the likely effect of particular price changes on the value of the RPI or CPI;
- use the RPI and/or the CPI to calculate the annual rate of inflation, the value of an index-linked pension and the purchasing power of the pound at one date compared with another;
- read and interpret data from a table, a graph or a diagram;
- understand the distinction between relative and absolute comparisons;
- understand the terms ‘ratio’, ‘proportion’ and ‘similar’, and use them appropriately;
- discuss the strengths and weaknesses of using words, tables, graphs and diagrams to present information;
- explain a familiar mathematical idea in your own words;
- understand the meaning of expressions such as Σ x and Σxw and use them.
- You should also be able to use your calculator to:
- clear exisitng data lists;
- enter data into lists and edit the data;
- find the median and the mean of a batch of data;
- find the mean of a batch of frequency data;
- find the weighted mean of a batch of data (with given weights);
- produce simple sequences of numbers.
This Unit looks at a wide variety of ways of comparing prices and the construction of a price index. You will look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You will also look at the important statistical and mathematical ideas that contribute to the construction of a price index.
In order to complete this Unit you will need to have obtained a Texas Instruments TI-83 calculator and the book Tapping into Mathematics With the TI-83 Graphics Calculator by Barrie Galpin and Alan Graham (eds), Addison Wesley, 1997 (ISBN 0201175479). This is referred to throughout the Unit as the Calculator Book.
This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offer in.
This is an extract from an Open University course which is no longer available to new students. If you found this interesting you could explore more free Mathematics Education course units or view the range of currently available OU Mathematics Education courses.