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 to make the task more straightforward, just look at the period from 1990 to 2004.
How might you use the ‘price of bread? measure as a way of investigating whether or not people got better off over this period?
In particular, think about:
the data you might wish to collect;
where you might look for the information you need.
The data used in Table 1 were taken from just two points in time. An alternative approach is to collect a series of values at regular intervals over the period in question. Suitable data indicating the price of bread in the UK can be found by looking on the UK Government Statistical Service website, which is at http://www.statistics.gov.uk [accessed 12 October 2006], and at a monthly publication there called Focus on Consumer Price Indices. Average prices for a selection of fairly standard goods are included each month. An example from the heading ‘Bread? is shown in Table 3.
| Type of loaf | Number of quotations | Average price (pence) | Price range containing 80% of quotations (pence) |
|---|---|---|---|
| 800 g white loaf, sliced | 349 | 55 | 39?76 |
| 800 g white loaf, unwrapped | 338 | 73 | 67?82 |
| 400 g white loaf, unsliced | 348 | 48 | 44?53 |
| 400 g brown loaf, sliced | 339 | 51 | 41?56 |
| 800 g brown loaf, unsliced | 331 | 77 | 73?84 |
A ‘quotation? here means a price, for the corresponding type of loaf, recorded in a survey of shops. So, for instance, prices for 800 g sliced white loaves were obtained at 349 shops.
First of all, you need to sort out what all these figures mean in order to select the information that is required.
(a) The information in Table 3 was gathered from a survey of shops. Roughly how many shops were surveyed? (Note, it is not the total of the numbers in the ‘Number of quotations? column.)
(b) On the basis of the average prices quoted here, what was the cheapest type of large (800 g) loaf?
(c) Using the information in the final column of the table and your common sense, estimate how much you might have to pay for one of the cheapest of the small brown loaves.
(d) How does presenting data in the form of a table help you to make sense of it?
(a) Assuming that quotations for all four types of loaf were obtained from each shop whenever possible, nearly 350 shops were surveyed. The number varies slightly from one type of loaf to another, presumably because not all shops stocked all these types of loaf.
(b) The cheapest type of large loaf, if we go by average prices, is the white sliced variety. However, given the variation in the quotations (in the final column of the table), you could actually pay more for a large white sliced loaf (for example, 89p) than for a 800g wholemeal sliced loaf (some of these cost as little as 60p). Notice, however, that the price range quoted in the final column of the table gives only the band within which 80% of the prices fell, presumably the middle 80% band of prices.
(c) The lowest price quoted here for the small brown loaf is 41p. However, note that the price ranges given in the final column of the table are those within which 80% of the quotations fell. It is quite likely, therefore, that there were some small brown loaves in the survey that were being sold for less than 41p (as well as some being sold for more than 56p).
(d) Tables can make information easy to find, and to read, if they are clearly laid out and well-labelled. They are compact, yet contain the ‘real? numbers. Tables help to structure the information, by selecting key features for the horizontal and vertical elements. However, when information has only been presented in table form, it can sometimes be hard to ‘un-table? it in your mind, in order to re-present it in some other form.
As you continue to work on this Unit, keep a note of how tables help you to process data.
Rather than the whole range of breads in Table 3, consider just one. The 55p average price for a large white sliced loaf has changed over the period 1990 to 2004. Table 4 below gives the corresponding average prices for this item in July over the period in question.
| Year | '90 | '91 | '92 | '93 | '94 | '95 | '96 | '97 | '98 | '99 | '00 | '01 | '02 | '03 | '04 |
| Price (p) | 50 | 54 | 53 | 55 | 50 | 53 | 55 | 53 | 52 | 51 | 52 | 50 | 58 | 58 | 65 |
It is not easy to see any clear pattern from these figures alone. It is often helpful to ‘re-present? numerical information using a different form: a graph. This is shown in Figure 1.
Figure 1 Graph of average July prices of a large white sliced loaf, 1990?2004Long descriptionThe two arrows on the graph point to the first plotted point, which corresponds to the first pair of values from Table 4, namely the year 1990 and the price 50 pence. The point is positioned by lining up the value 1990 on the ‘Year? axis and the value 50 on the ‘Price per loaf/pence? axis. Each of the other points is plotted using the same principle.
(a) The adjacent points on this graph Figure 1 have been joined with straight lines. What is the meaning of these lines and why is this procedure appropriate in this example?
(b) Some parts of the graph show a steeper slope than others. Identify intervals of time where the graph is particularly steep and explain what this signifies.
(a) Adjacent points on the graph refer to the July prices, in successive years, of a large white sliced loaf. Joining two adjacent points allows you to make a reasonable guess at the bread prices during the intervening months. The procedure of joining up the dots is valid here because the prices vary slowly over time and time is measured on a continuous scale. With certain other sorts of graph it would not be legitimate.
(b) The steepest upward-sloping parts of the graph are from 2001 to 2002 and from 2003 to 2004. There is also a fairly steep downturn from 1993 to 1994. These sections show that the price of bread changed more in a single year than during other years between 1990 and 2004.
In Table 4, and in Figure 1, the same information is presented in two different ways. There are many occasions when going backwards and forwards between a table and a diagram is helpful, because different ways of representing data stress and ignore different things.
Now think more generally about tables and graphs that you have seen in the world of represented data around you. How do different forms of image enable you to make sense of the data represented? Are there any advantages in portraying information by means of a graph, as opposed to a table or in words? Does your answer depend on the purpose for which the information is required?
When presenting results and data it is important to think about the most appropriate method for displaying the work for ease of use. Thinking about and discussing the advantages and disadvantages of different methods helps you to become more critical in displaying and presenting your own data.
It should be clear from Figure 1 that bread prices rose over this fifteen-year period. However, the rate of increase has not been steady: for example, over the year between July 1990 and July 1991, the graph shows a moderately steep increase, and then did not change much for the next two years, before falling back fairly steeply from July 1993 to July 1994, so that its 1994 level was the same as its 1990 level. After July 1994, the price rose again for two years, but then gradually declined and in July 2001 it was again at its 1994 level. Since July 2001 the price has risen fairly steeply.
Now return to Table 4 to check more carefully some of the details and further implications. Between July 2003 and July 2004, the price of an 800g sliced white loaf went up by 7p.
Over the same period, the average price of 50kg of coal went up by 8p, from £8.19 to £8.27. You might say that the price increase for coal was more than that for bread. While this is a correct statement, it is rather misleading. To take a more extreme case, an increase of 10p in the price of a newspaper is far more important than an increase of 10p in the price of a new car. A more informative way of describing price rises is to express them as proportions or percentages of the original price of the item in question. So if a newspaper costing 50p went up in price by 10p, this would represent an increase of one-fifth, or 20% of its original price, whereas 10p on the price of a £10,000 car is an increase of only 0.001%.
Calculate the proportional and the percentage increase in the average bread price from 2003 to 2004, using your calculator as follows.
Divide the price increase, 7p, by the original price, 58p, to give the proportional increase. Then multiply by 100% to turn the answer into a percentage increase.
Thus the proportional increase is
Long descriptionEquation showing the working to calculate the proportion increase in the average bread price from 2003 to 2004 of 0.12
The percentage increase is
Long descriptionNotice the symbol in the figure above, which means ‘is approximately equal to?. It is similar to the equals sign, but it serves as a reminder that rounding or some other means of approximation has been used — in this case, the percentage is rounded to the nearest whole number.
(a) Using the same approach as for the calculation above, use the data given above to work out the proportional increase and the percentage increase in the average price of 50kg of coal between July 2003 and July 2004.
(b) How would you now modify the earlier statement that ‘the price increase for coal was more than that for bread??
(c) Using data from Table 4 calculate the percentage increase in the average price of a large white sliced loaf between July 1990 and July 2003.
(a) Coal prices (for 50kg) went up by 8p (from 819p to 827p) between July 2003 and July 2004. Expressed as a proportion of the July 2003 price, this is
Long description
As a percentage of the July 2003 price, the increase is
Long description
(b) The increase in the price of bread (from July 2003 to July 2004) was 12%. The increase in the price of coal (over the same period) was 1%.
When expressed in percentage terms, the first price increase was about twelve times as much as the second one.
(c) Bread prices went up by 8p (from 50p to 58p) between July 1990 and July 2003. Expressed as a percentage of the July 1990 price, this is
Long description
How have wage rates changed over the same period? Have a look at Table 5, below.
| Year | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 |
| Rate (£) | 295.6 | 318.2 | 340.1 | 353.5 | 362.1 | 374.6 | 391.3 | 408.7 | 427.1 | 442.4 | 464.1 | 490.5 | 513.8 | 525.0 |
These figures refer to the average (mean) gross full-time earnings including overtime, for those men whose pay was not affected by absence. The mean is discussed in Section 2 of this Unit. Data for 2004 are not available on the same basis as these data for 1990?2003
(a) Calculate the percentage increase in average male weekly earnings between 1990 and 2003.
(b) Compare your answer for part (a) with your answer for part (c) of Activity 7. What conclusions can you draw by comparing these two values?
(a) Average weekly earnings went up by £229.4 (from £295.6 to £525.0) between 1990 and 2003. Expressed as a percentage of 1990 earnings, this is
Long description
This is a substantial increase. Average weekly earnings have gone up by more than three-quarters of their 1990 value.
(b) Average male earnings have gone up much more than the average price of bread. See also the comments in the text following this activity.
Overall, the results of the various calculations in the previous two activities seem to suggest that, while bread prices and male earnings both rose throughout the period in question, male weekly earnings rose much more in percentage terms than bread prices. So does this prove ‘we were all better off in 2003 than in 1990??
There are several reasons that such a conclusion does not necessarily follow.
First, the earnings figures refer only to men in Great Britain. They do not relate to women, or to anyone in Northern Ireland.
Second, the earnings figures are averaged out over a wide range of jobs. Some workers may be better off, others may be worse off.
Third, not everyone was in employment. In fact, over the period in question, the percentage of the workforce who were unemployed fluctuated between about 5% and 11%. So, for the one and a half million unemployed people in 2003 (or roughly one in twenty of the work force), this average rate of pay of £525 per week would be a complete irrelevance.
A fourth source of doubt is that changes in bread prices alone are a poor measure of how prices have changed as a whole. Bread purchases represent only a small fraction of typical weekly shopping baskets, and so we really need to take account of a much wider range of goods. How to choose and analyse a suitable basket of goods is the central issue of the next subsection.
The main aim of Subsections 2.1 and 2.2 has been to pose the central question of how to assess whether people are materially better off today than in the past. Data were collected and analysed and some interpretations were made of the results of this analysis. At this stage, one conclusion seems to be that, in general terms, we have become better off. However, this conclusion is only tentative, for you have seen how a superficial quantitative approach can be misleading. There are more formal and more accurate ways of investigating this central question: in particular, there are crucial measures of prices and of earnings. The rest of this section concentrates on prices; the next section looks at earnings.
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