| Retail Price Index | Statistics In Your World |
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| Student Notes |
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| Brief Description Aims and Objectives Prerequisites Equipment and Planning Section A |
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Brief Description This unit introduces pupils to the concept of an index number. It starts with price relatives for individual items, builds up to calculating a weighted index number, and has a final section working out the Retail Price Index and looking at the groups of items involved. Design Time: 5-6 hours Aims and Objectives After completing the unit the pupil should be familiar with the terms index number, base year, weights, the Retail Price Index, its meaning and the categories making up the Index. They should be able to calculate a price relative (called index number in the pupil unit) for an individual item and for a number of unweighted items; calculate weights using frequency of purchase and use these weights to calculate a weighted price index; and calculate a retail price index given individual indices, or values in the base year and the current year. They practice completing tables, collecting data from home (and optionally from shops in a survey of local prices) and calculating an arithmetic mean. Prerequisites Pupils must be familiar with ratios and percentages and be able to calculate an arithmetic mean. Division by up to three digits will be encountered, and calculators would ease the arithmetic. D2a is easier if pupils have met simple flow charts Equipment and Planning Calculators are strongly recommended. Prices for 1977 and 1978 are given throughout the unit. Many sections refer to this year’s prices and last year’s prices to keep the unit up-to-date. Teachers should be prepared for some discussion as to what these prices are, especially in Sections A3, A4 and B3. The optional survey in Section C2 can be carried out at any time before Section C3 and the current prices put on Table 9. If done early enough, these prices can be used for Section A4. Section C3 and D1 require pupils to get simple patterns of family expenditure from home, and this will need some preliminary discussion with them. Pupils should work in whole pence throughout the unit, except in Section D. Otherwise they will have difficulty with, for example, £129 ÷ 89p. Some prices are given in Table 9 in the pupil unit. Because of seasonal and’ local variations, it may be preferable to use local, up-to-date prices. National ‘shopping baskets’ are given in a few daily papers such as the Guardian and the Daily Mirror. What we have called the Retail Price Index is properly called the General Index of Retail Prices (G.I.R.P.). Section A The work could be introduced by a class discussion on pocket money and its increase from last year to this year. The variety of answers can lead on to considering which increase is the most appropriate. Earnings from part-time work and increases because of age should be ignored. Eventually discussion will centre on price increases. One possible answer is: ‘The new amount should buy the same items as last year’. This theme is developed. Al The price increase is compared with the percentage calculation. The figures are approximate to give an easy calculation. The largest increase is not the greatest percentage increase. INDEX NUMBER and BASE YEAR are introduced. More able pupils may appreciate that an index number of 130 means an increase of 30%. *A2 This section is optional and provides less able pupils with more practice in finding individual price indices. The calculator has decreased in price so that it has an index number less than 100. A3 This section introduces an unweighted price index of three items. The numbers begin to be more difficult to handle without a calculator. The one-year’s price rises calculated can be compared with the pocket money rise, but a fair comparison is only possible with the later weighted price index. A4 As a step towards the Retail Price Index, we look at a simple grocery price index. Present-day prices are compared back to 1977 as a base year. If today’s prices are not available, the 1978 prices of Table 9 can be used. The Guardian or Daily Mirror monthly shopping basket can be useful here. Section B B1 The 2p increase will have a different effect on items bought with different frequency. The 2p increase on bread is more important, since more loaves of bread are bought than Sunday joints. This section could well be a discussion session to bring out this point. The weights here are taken as the frequencies of purchase in a week (or possibly fortnight or month). From G.I.R.P. in 1977, bread rose 17%, butter rose 4%, jam, etc., rose 10%. The overall percentage increase in a slice of bread and jam is a complex amalgam of these three percentages, which may differ greatly from the bread index. B2 This could be a class example. Notice that the weights mean we compare total costs for weeks in the two years. B3 Here pupils use their own figures to work out a weighted price index over the past year. This can be compared with the index showing pocket money increase over the year, calculated in A3. B4 By using the individual index numbers and the weekly costs (not prices) of each item, the weighted index can be worked out. This section is important since it is essentially this method which is used to work out the G.I.R.P. The costs come from sources such as the Family Expenditure Survey, and the individual index numbers (more properly called price relatives) come from a prices survey. It is important to notice that the weighted index is not the mean of the three price relatives: i.e. not (113 + 130 + 120)/3 which is exactly 121. The true value is 120.62. Section C This section requires Table 9 on page R2 for each pupil. Results should be handed in for comparison in C3. This section looks at grocery prices in more detail and includes a survey (optional) in local shops. Cl Table 9 is used to reinforce B3. C1c may need some more explanation, e.g. items bought monthly could be given a weight of 1/4. *C2 This is an optional survey to determine shop prices. Each person can concentrate on an individual item and the results can then be put together to form several shopping lists from each shop, and also give the average prices. A possible table to record results is given below.
C3 The weights obtained from home may only be approximate. If the costs from each family for each item are handed in, the class totals are a kind of Family Expenditure Survey. There are two alternative sets of questions in this section. Questions b, c and d give an up-to-date estimate of the food index using the present-day costs found in C2, with 1977 as base year. If C2 is not done, then questions e, f and g give the 1978 food index, with 1977 as base year. A sheet for collecting the class data needs to be prepared, although this can be done (but with less confidentiality and taking more time) on the blackboard. *C4 This section shows how to find a combined index without weights, using instead the total costs of each item in the base year with the individual price indices. This reflects how an index is actually worked out. It is much easier to keep track of total expenditure on individual items rather than to record how often they are bought. Thus it is easier to record the total weekly cost of bread, since a family may buy different sorts each week at different prices. Also prices change relatively frequently, whereas weights can only be worked out annually. Thus the weights used do represent total expenditure. This has the added advantage that changing preferences are automatically recorded each year. Some teachers may prefer to begin with this method rather than by using weights explicitly. It reinforces the work first introduced in B4, and is used again in Section D3 to work out the Retail Price Index. Section D This final section broadens the index to other commodities. Dl and D2 These could be tackled in groups. The questions are general. They are answered specifically in D3. Thus D3 should not be looked at before completing these questions. Pupils may need some guidance with Die. D3 Mr Hill’s costs represent the weights used during 1978 by the Department of Employment to calculate the Retail Price Index. The actual individual indices are for January 1978, using January 1977 as the base time. It is interesting to note the individual indices and see how items have gone up. For further practice one could work out indices from various categories grouped together, e.g. housing, fuel and light and durable household goods or alcoholic drink and tobacco. The Retail Price Index is published in the Monthly Digest of Statistics and more fully in the Department of Employment Gazette (HMSO). In particular in March of each year the Gazette gives full details of changes over the previous year. Information on how the index has changed since 1962 is also given. Another useful source is Method of Construction and Calculation of the Index of Retail Prices (HMSO).
February, 1978 A plain man’s guide to the family expenditure survey, pages 137-147. Technical improvement in the retail prices index, pages 148-150. Method of Construction and Calculation of the Index of Retail Prices (HMSO) Monthly Digest of Statistics(HMSO) M J. Moroney, Facts from Figures, pages 48-54, (Penguin, 1951) W J Reichmann, Use and Abuse of Statistics, Chapter 12, pages 152-171 (Penguin, 1964) Answers Al a Bus fare 2p, Coca-cola 1p, chocolate 6p, yoghourt 2p b Chocolate c 5 d l30p e Bus fare 140, Coca-cola 125, chocolate 130, yoghourt 125 f Bus fare g No. The biggest increase is on the most costly item and is not the biggest percentage increase. i. As e *A2 b Disco 117, fish and chips 120, youth club 130, swimming 133, cinema 108, calculator 90 C Fish and chips d Swimming D3 a Alcoholic drink: Beer, cider, wine, spirits etc.
RPI = 1101/1000 * 100 = 110.1 Test Questions The price of an ice lolly was l0p in 1977. In 1978 it cost 12p. a Write down the actual price increase. The price of an ice lolly was l0p in 1977. In 1978 it cost 12p. a Write down the actual price increase. 2 Use the following table to answer the questions below it.
b Which item had the greatest actual price increase? c Which item had the greatest percentage price increase? d Explain why your answer to b is not the same as your answer to c. 3 Use the following table to answer the questions below it.
a Explain the word ‘weights’ as used in the table. b Work out the missing numbers and complete the table. c Work out the weighted index number (to the nearest whole number) for 1979, based on the weekly total for 1977. d If Tracy received £1 pocket money in 1977, how much should she have received in 1979 to maintain her same standards? e If her pocket money did not increase, would the table still fairly represent her expenditure? Why? 4 a What does the Retail Price Index actually show? Test Questions: Answers 1 a 2p b 120 c 14.5p 2 a 160, 150, 155, 138 (or 137.5) 3 a In this example a weight is the frequency with which that item is
purchased in one week. 4 a The amount, expressed in percentage terms, that would need to be
spent to purchase the same amount of goods and services as were purchased in the base
year. Resource (R) Pages Table 7 Pocket Money Price Index
Table 8 Grocery Prices
Table 9 Grocery Prices
Connections with Other Units Other Units at the Same Level (Level 4) Choice or Chance, Testing Testing, Figuring the Future, Smoking and Health, Sampling the Census, Equal Pay. Units at Other Levels In the Same or Allied Areas of the Curriculum Level 1 Leisure for Pleasure Level 2 On the Ball, Opinion Matters Level 3 Cutting it Fine, Pupil Poll, Car Careers, Multiplying People. This unit is particularly relevant to: Economics, Commerce, Social Sciences, Humanities, Mathematics. Interconnections between concepts and techniques used in these units These are detailed in the following table. The code number in the left-hand column refers to the items spelled out in more detail in Chapter 5 of Teaching Statistics 11-16. An item mentioned under Statistical Prerequisites needs to be covered before this unit is taught. Units which introduce this idea or technique are listed alongside. An item mentioned under Idea or Technique Used is not specifically introduced or necessarily pointed out as such in the unit. There may be one or more specific examples of a more general concept. No previous experience is necessary with these items before teaching the unit, but more practice can be obtained before or afterwards by using the other units listed in the two columns alongside. An item mentioned under Idea or Technique Introduced occurs specifically in the unit and, if a technique, there will be specific detailed instruction for carrying it out. Further practice and reinforcement can be carried out by using the other units listed alongside.
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