Basic Engineering Mathematics, Fifth Edition

Presentation of statistical data 291

subdivided into the values in the table of percentages
shown above. A key is used (different types of shading
or different colour schemes) to indicate corresponding
percentage values in the rows of the table of percent-
ages. The percentage component bar chart is shown in
Figure 31.4.

1

10

Percentage relative frequency^20

30

40

50

60

70

80

90

100

23

Year

Key

6-roomed houses

5-roomed houses

4-roomed houses

5-roomed bungalows

4-roomed bungalows

Figure 31.4

Problem 6. The retail price of a product costing

£2 is made up as follows: materials 10p, labour

20p, research and development 40p, overheads

70p, profit 60p. Present these data on a pie diagram

A circle of any radius is drawn. The area of the circle
represents the whole, which in this case is £2. The circle
is subdivided into sectors so that the areas of the sectors
are proportional to the parts; i.e., the parts which make
up the total retail price. For the area of a sector to be
proportionaltoa part, the angle at the centre of the circle
must be proportional to thatpart. The whole, £2 or 200p,
corresponds to 360◦. Therefore,

10p corresponds to 360×

10

200

degrees, i.e. 18◦

20p corresponds to 360×

20

200

degrees, i.e. 36◦

and so on, giving the angles at the centre of the circle
for the parts of the retail price as 18◦, 36 ◦, 72 ◦, 126 ◦and
108 ◦, respectively.
The pie diagram is shown in Figure 31.5.

Problem 7.

(a) Using the data given in Figure 31.2 only,

calculate the amount of money paid toeach

salesman for travelling expenses if they are

paid an allowance of 37p per mile.

1088

Ip ; 1.8 8

188

(^728368)
1268
Overheads
Profit
Labour
Research and
development
Materials
Figure 31.5
(b) Using the data presented in Figure 31.4,
comment on the housing trends over the
three-year period.
(c) Determine the profit made by selling 700 units
of the product shown in Figure 31.5
(a) By measuring the length of rectangle P,the
mileage covered by salesmanPis equivalent to
413 miles. HencesalesmanPreceives a travelling
allowance of
£413× 37
100
i.e.£152. 81
Similarly, forsalesmanQ, the miles travelled are
264 and his allowance is
£264× 37
100
i.e.£97. 68
SalesmanRtravels 597 miles and he receives
£597× 37
100
i.e.£220. 89
Finally,salesmanSreceives
£143× 37
100
i.e.£52. 91
(b) An analysis of Figure 31.4 shows that 5-roomed
bungalows and 5-roomed houses are becoming
morepopular,thegreatest changeinthethreeyears
being a 15% increase in the sales of 5-roomed
bungalows.
(c) Since 1. 8 ◦corresponds to 1p and the profit occu-
pies 108◦of the pie diagram, the profit per unit is
108 × 1

1. 8
   i.e. 60p
   The profit when selling 700 units of the prod-
   uct is
   £
   700 × 60
   100
   i.e.£420