Prices

1.2.3: A typical shopping basket

This subsection discusses using a typical basket of goods to analyse price changes over time. However, what is meant by ‘typical??

Think back to the last time you went shopping. What did you buy? The electric light bulbs that you have just stocked up on are unlikely to be in your shopping basket next week, whereas milk may well be there every week. And there may be items—a new toothbrush for example—that you buy from time to time, but not this week.

To monitor price changes in a way that takes account of all goods, it is not enough merely to consider those items that you buy in a supermarket in any particular week. Suppose, for example, that you had bought a new bicycle. This would ensure that bicycle expenditures would be included. But the cost of the bicycle is likely to outweigh everything else in your ‘shopping basket? and would give bicycle expenditure undue importance in your weekly budget.

So, merely taking one person's basket for one particular week is actually not likely to be typical. In order to make a thorough job of finding a ‘typical? shopping basket, you would really need to take a sample of different people and follow their purchases over a period of weeks or months. This is actually done by the UK government organisation which monitors price changes, and the procedure is described in more detail in Section 5 of this Unit.

However, for reasons of simplicity, this section concentrates on a small ‘shopping basket? containing just five items of food bought by a large proportion of households in the UK. It will illustrate some of the main ideas involved in measuring and comparing price changes. The five food items chosen here are bread, milk, eggs, potatoes and sugar.

Here is a first attempt at calculating some sort of average price increase over the fourteen-year period from July 1990 to July 2004. The data are given in Table 6 and have been quoted to the nearest penny.

Table 6 1990 and 2004 prices for a small basket of goods

One way of finding an average or typical value is to calculate the mean. Divide the total increase by the number of items.

In this case, the average (mean) price rise of the five items is

• Look at the calculation above. Do you feel the answer is useful as a measure of an average price increase? Explain why or why not.

You may or may not have noticed that this calculation is rather unhelpful and the result of ‘29.2p? is consequently a pretty meaningless figure. To demonstrate this, suppose that the potatoes happened to be bought as a 50 kg sack, rather than as one kilogram. Under these circumstances, the calculation would be as shown in Table 7.

Table 7 1990 and 2004 prices for a basket containing a large sack of potatoes

So, simply altering the units in which the potatoes have been bought has made a dramatic difference to the average price increase. The same problem applies to all the other items. Why choose the unit of milk as one pint? You could have chosen one litre, or four pints, or anything at all. Similarly, there is nothing special about choosing a dozen eggs. The amount could have been half a dozen or 144 or something else.

The quantity of each item that is chosen is crucially important to this calculation, as it determines the ‘weighting? of that item in the overall average.

• What might be a fairer way of choosing a suitable weighting for an item?

As discussed in the previous subsection, one possibility is to dispense with price increases expressed in pounds and pence and work only with proportional or percentage increases for each item.

The proportional price increase is the price increase divided by the original price. The percentage price increase is the proportional price increase multiplied by 100%:

Another attempt at calculating a measure of the average price increase over the fourteen-year period from 1990 to 2004 is shown in Table 8. The proportional price increases are given correct to two decimal places, and the percentage increases in the table are given to the nearest whole percentage.

Table 8 Calculating proportional and percentage price increases for a small basket of goods

Item	July 1990 price	July 2004 price	Increase	Proportional increase (2 d.p.)	% increase (nearest %)
Large loaf (white)	50p	65p	15p
Milk (lpint, pasteurised)	30p	35p	5p
Eggs (1 dozen, size 2)	121p	169p	48p
Potatoes (1 kg, new loose)	29p	96p	67p
Sugar (1 kg)	63p	74p	11p
Total				3.35	335%

Average proportional price increase is , and percentage price increase is .

• Look at the calculations above. How useful do you feel these answers are as measures of an average proportional and percentage price increase?

These attempts at calculating an average price increase make an improvement in one respect. Dealing only with proportions and percentages has solved the problem of having to decide in which units to measure each item—the proportional price rise of potatoes is 2.31, regardless of whether they were bought in amounts of 1 kg or 50 kg. However, the final stage of the calculation, which involved adding the five proportions or percentages together and dividing by five, has resulted in giving each item the same emphasis. As a measure of how these price changes affect the standard of living, this may not be very sensible. Different items may well have different impacts on someone's budget. For example, you may consume one pint of milk per day but use much less than 1 kg of sugar.

In everyday language, people often talk about emphasis in terms of ‘weighting? one thing more heavily than another. This physical image is quite helpful to bear in mind. The idea is to adjust the effect of different values to produce a combined average measure (called a weighted mean). You can alter the relative emphasis placed among the values by multiplying them by a set of numbers called weights. For example, you can make one value twice as important as others by multiplying it by two before adding it in. The term ‘weight? refers to the number attached to each item to indicate its relative importance.

Weights and weighting

Note that in this context the terms ‘weight? and ‘weighting? mean the same thing, but the word ‘weight? rather than ‘weighting? is used here, because this is the term usually used in the calculation of inflation. The term ‘weight? will be used, here and in other Units, in this technical sense. Note that this is quite different from the everyday meaning of the weight of goods in the shopping basket as a measure of ‘heaviness?.

Activity 9: Choosing a suitable weighting

Assume that the five items listed earlier make up a suitable ‘basket of goods? for estimating average percentage price increases. What do you think would be a sensible set of ‘weights? to choose for each item in order to calculate a meaningful average?

The most immediate weights to choose are probably the amounts of money spent on each item by a typical household over a typical week. These are the weights chosen by the government in their calculations and this is the approach adopted here.

In order to continue the discussion of the use of weights to find the ‘average? price increase of a basket of goods, you need to look at the calculation of averages in general. As you will see in the next section, the idea of a weight can then be incorporated into the calculation of a particular sort of average, called the weighted mean.

Outcomes

After studying this section, you should be able to:

• ♦ consider and decide what data are required to make comparisons of prices (Activities 1 and 9);

• ♦ calculate a proportion, a percentage, a proportional increase and a percentage increase (Activities 3, 7 and 8);

• ♦ read and interpret data from a table (Activities 2 and 4);

• ♦ read and interpret information from a graph (Activity 5);

• ♦ make some comments about the differences between representing data by tables and by graphs (Activity 6);

• ♦ appreciate the need to choose suitable ‘weights? when calculating-average values in certain situations (Activity 9).

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