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Topic outline

 

  • Time: 20 hours
    Level: Introductory

 
 

Introduction

  • Introduction Resource
  • 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...
 

1: Introduction

  • 1: Introduction Resource
  • Are we getting better off? Politicians and journalists often make sweeping claims about whether or not ‘we’ are getting better off.
 

2: Are we getting better off?

  • 2.1: Using your loaf Resource
  • Cade: There shall be in England seven halfpenny loaves sold for a penny; the three-hooped pot shall have ten hoops; and I will make it felony to drink small beer.
  • 2.2: The price of a loaf these days Resource
  • The investigation so far illustrates just how difficult it can be to make a fair comparison of prices. In this subsection, the central question is still ‘Are people getting better off?’ However, in order...
  • 2.3: A typical shopping basket Resource
  • This subsection discusses using a typical basket of goods to analyse price changes over time. However, what is meant by ‘typical’?
 

3: A statistical interlude—averages

 

4: Price ratios and price indices

  • 4.1: Price ratios Resource
  • In Chapter 1, Section 1.4 of the Calculator Book, you saw that multiplying a price by, say, 1.30 is equivalent to increasing it by 30%. Similarly, multiplying a price by 0.94 is equivalent to decreasing...
  • 4.2: Price indices Resource
  • 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...
 

5: The UK Government price indices

  • 5.1: What are the CPI and RPI? Resource
  • The Consumer Prices Index (CPI) and the Retail Prices Index (RPI) are published each month by the UK Office for National Statistics. These are the main measures used in the UK to record changes in the...
  • 5.2: Calculating the price indices Resource
  • This subsection concentrates on how the RPI is calculated. Generally the CPI is calculated in a similar way, though some of the details differ. To measure price changes in general, it is sufficient to...
 

6: Using the price indices

 

7: Some mathematical themes

  • 7.1:Relative and absolute comparisons Resource
  • The distinction between relative and absolute comparisons is an important one that has run through this Unit. Here, its meaning and significance will be made more explicit. The subsection begins with examples...
  • 7.2: Ratio and proportion Resource
  • It is easy to distinguish children from adults. For one thing, children are usually much smaller. But how are we able to tell them apart from a drawing alone? Have a look at the two outline drawings. Which...
  • 7.3: Is a picture worth a thousand words? Resource
  • This final subsection is an overview of the various modes of mathematical communication used so far, like words, tables and graphs, and diagrams. You may have a preference for one over the others as a...
 

8: Summary

  • 8: Summary Resource
  • This Unit has looked at a variety of ways of comparing prices, and the construction of a price index. Important statistical ideas that contributed to this included mean, weighted mean and median, as well...
 

References and Acknowledgements

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