As the diagrams are drawn accurately we can measure the radius of each pie chart and use these to find the ratio of the areas (and so the populations) of Adley and Bridford.

6-2-hard-q1-1

The area of a circle is given by the formula $A = π r^{2}$ .

Area of Adley pie chart $= π {(5)}^{2} = 25 π$

[1]

Area of Bridford pie chart $= π {(4)}^{2} = 16 π$

So the ratio of the populations of Adley to Bridford ( $A : B$ ) is

$A : B = 25 π : 16 π = 25 : 16$

and so the fraction of people living in Adley is

$\frac{25}{25 + 16} = \frac{25}{41}$

Measure the angle of the 0 - 19 category on the Adley pie chart so we can work out the fraction of people living in Adley who are aged 0 - 19.

6-2-hard-q1-2

$\frac{70}{360} = \frac{7}{36}$

To find the proportion of people (out of the two towns) who live in Adley AND are aged 0 - 19 we need to find the product of these two fractions.

$\frac{25}{41} \times \frac{7}{36} = \frac{175}{1476}$

[1]

This is an awkward fraction so the answer is best given as a percentage.
To change $\frac{175}{1476}$ to a percentage use your calculator to convert it to a decimal, and then multiply by 100.

$\frac{175}{1476} \times 100 % = 11.856 . . .$

Round your final answer to a sensible degree of accuracy, three significant figures is often used.

Proportion of people living in Adley and aged 0 - 19 years is 11.9% (3 s.f.) [1]

Travel to school	Number of children
Walk	12
Car	7
Bicycle	9
Bus	4

Travel to school	Number of children	Pie chart angle
Walk	18
Car	3
Bus	9

Choice	Number of students
University	57
Training	45
Work	18

Number of cinema visits	0	1	2	3	4	5	6	7
Frequency	5	6	6	6	7	3	6	2

Bird	Frequency
Magpie	15
Thrush	10
Startling	20
Sparrow	27

Statistical Diagrams (Cambridge O Level Maths)

Exam Questions