5.4 Data analysis and inference 227
or £1.87 billion. The pie chart shows
that individuals contribute 61% of all
donations to medical research charities,
so the total donations must amount to
= £3.07 billion.
4 This is explained by the fact that a small
number of charities receive very large
incomes: there will be a large number
of medical research charities, some of
which will be very small so will not
contribute to the 6%, that receive 90%
of the income. The 6% will be made up
of a small number of charities in the top
few categories. In the lower parts of the
chart, there will be a huge number of
very specialised charities receiving very
small incomes. The numbers on the
chart do not relate to the numbers of
charities, only to the proportions.
One final repeated warning: correlation does
not always mean cause and effect. Sometimes
two variables appear to correlate, but one does
not lead to the other. The correlation may be
coincidental, a statistical fluke, or both
observations may be caused by a third factor.
One classic example is that there is a close
correlation between ice cream sales and deaths
due to drowning. It would be ridiculous to say
that either of these is a cause of the other. In
fact, they both increase during hot weather.
Many similar examples can be found.• Complex data sets have been introduced
which require a range of skills to analyse.
• We have seen that it is necessary to
process data – grouping, averaging and so
on – and sometimes to graph data in order
to identify patterns and trends which may
be used to draw conclusions.
• We have seen that extended examples where
more data is supplied can require analysis
that may lead to a range of conclusions.Summary
Commentary
1 The bar chart shows the percentage of
people who donate and the percentage
of total donations. Thus the type of
charity with the highest proportion of
donations relative to the proportion of
people contributing will get the highest
average donation and vice versa. On this
basis, the charity type receiving the
highest average contribution is religious
organisations (the only one for which the
percentage of total donations exceeds
the percentage of people contributing).
2 The charity type with the lowest average
donation is homeless (3 : 1 ratio). The
only other charity type approaching this
is disabled (approximately 2.75 : 1).
3 Individual donations to medical research
charities amount to 17% of £11 billion,
The sources of all income for medical
charities are shown in the pie chart.Public
sector 4%Private
sector 2%Voluntary
sector 7%Internally
generated 26%
Individuals
61%Answer the following questions and give brief
explanations of your answers.
1 For which type of charity do individuals
donate the largest average amount?
2 For which type of charity do individuals
donate the smallest average amount?
3 What is the estimated total income of
medical research charities?
4 It has been stated elsewhere that 6%
of charities receive 90% of the total
income, yet medical research, the largest
beneficiary, accounts for 17% of donations.
Explain this.