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 which illustrate the difference between absolute and relative measures, and you will be asked to reflect on why calculating in relative terms is often a better way to make a fair comparison.
Start with a simple example based on comparison of births between countries. In 2002, there were roughly 60 000 babies born in the Republic of Ireland and 670 000 born in the UK. So, in absolute terms, there are many more births in the UK (670 000 is far more than 60 000), but so what? The population of the UK is much greater than that of the Republic of Ireland, so this difference is not unexpected. A more useful and interesting comparison is the birth rates of the two countries, and for this, additional data are required.
| Births | Population in millions | |
|---|---|---|
| Republic of Ireland | 60 000 | 3.9 |
| UK | 670 000 | 59.1 |
The birth rate is normally calculated as the number of births per 1000 of the population.
The birth rate for the Republic of Ireland in 2002 was 60 000
(a) Use Table 24 to calculate the UK birth rate. Give your answer to the nearest whole number.
(b) How do the birth rates for the Republic of Ireland and the UK compare?
(a) In 2002, the birth rate for the UK was
(b) The birth rates are actually more similar than are the numbers of births. Though Ireland has a much small absolute number of births, it has the higher birth rate.
The point of the previous activity was to re-emphasise that absolute comparisons, like that between the numbers of births, are often not very helpful, and that a relative comparison, like that of the birth rates, is usually more meaningful. Here is another activity designed to reinforce this point.
Between 1993 and 2003, UK government spending on Transport rose from £10.6 billion to £13.6 billion. Over the same period, total government expenditure on services rose from £270.1 billion to £399.5 billion. 1 billion = 109 (Source: Public Expenditure Statistical Analysis 2004, p.39, Table 3.2)
(a) Use the data above to make a case that the government has done well in its provision of transport services over this period. You might like to try writing this case in the style that a newspaper journalist might use.
(b) Use the data above to make a case that the government has done badly in its provision of transport services over this period. Again, you might like to try writing in the style of a newspaper journalist.
More detail has been included in this comment than you would have been expected to produce.
(a) This first ‘newspaper cutting? praises government performance. Note that it does so by ignoring total government spending and inflation over the period in question.
Massive increase of nearly one third in just nine years
Government spending on transport rose from £10.6 billion to £13.6 billion, a massive increase of £3 billion, or 28% in just nine years. This figure of £13.6 billion represents a spending of £230 for each man woman and child throughout the length and breadth of the UK.
(b) This second ‘newspaper cutting? criticises government performance. Note that it does so by ignoring the absolute increase in government spending on transport over the period in question.
Chancellor, can I have my thirty-five quid back please?
In 1993, out of every £1 it spent, the government spent a miserly 3.9 pence on transport. By 2003, this figure had fallen to 3.4 pence, a drop of 13%. Based on 2003 government spending figures, this represents a loss to the public of a massive £2.1 billion, or £35 for every man, woman and child up and down the country. So, please, Mr Chancellor, can I have my £35 back?
The distinction between absolute and relative difference can be represented graphically, as follows.
Figure 3 Pie charts showing UK government spending on ‘Transport? as a percentage of total government expenditure on services in 1993 and 2003. (Note that the circles have been drawn so that their areas are in proportion to the total government spending for each year.)Long descriptionAs the diagram shows, in absolute terms, there is more ‘cake? in the shaded slice for 2003 than for 1993 (spending has gone up from £10.6 billion to £13.6billion). But relatively speaking, the transport slice is smaller in proportion to total expenditure in 2003—it has fallen from 3.9% to 3.4% of the overall cake.
Pie charts offer another kind of graphical image. You could add details of pie charts to the notes that you made for Activity 6.
The strength of using relative measures, such as ratios and percentages, is that they take account of the size of the base from which the measure is taken. However, there is a weakness in this approach as well, in that there may be a loss of valuable information. For example, an American newspaper once claimed that a survey had shown 60% of the electorate to be in favour of a particular candidate. What the journalist did not reveal at the time was that his ‘survey? consisted of five men in a bar (whom he had asked the previous evening), three of whom had expressed a preference for the candidate in question. Similarly, if someone earning £5000 a year and someone earning £50 000 a year both get a 5% pay rise, is this ‘fair? ? (Equal percentage rises widen absolute differences).
Nevertheless, although percentages too may not always have the desired effect or be misleading, overall, expressing measures as ratios (one number divided by another) is a powerful idea in mathematics across a range of mathematical concepts.
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