Higher Engineering Mathematics

530 STATISTICS AND PROBABILITY

Figure 54.4

area of a sector to be proportional to a part, the angle
at the centre of the circle must be proportional to that
part. The whole, £2 or 200 p, corresponds to 360◦.
Therefore,

10 p corresponds to 360×

10

200

degrees, i.e. 18◦

20 p 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 Fig. 54.5.

Figure 54.5

Problem 7.

(a) Using the data given in Fig. 54.2 only, cal-

culate the amount of money paid to each

salesman for travelling expenses, if they are

paid an allowance of 37 p per mile.

(b) Using the data presented in Fig. 54.4, com-

ment on the housing trends over the three-

year period.

(c) Determine the profit made by selling 700

units of the product shown in Fig. 54.5.

(a) By measuring the length of rectangleP the

mileage covered by salesmanPis equivalent

to 413 miles. Hence salesmanP receives a

travelling allowance of

£413× 37

100

, i.e.£152. 81

Similarly, for salesmanQ, 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 Fig. 54.4 shows that 5-roomed

bungalows and 5-roomed houses are becom-

ing more popular, the greatest change in the

three years being a 15% increase in the sales of

5-roomed bungalows.

(c) Since 1.8◦corresponds to 1 p and the profit

occupies 108◦of the pie diagram, then the profit

per unit is

108 × 1

1. 8

, that is, 60 p

The profit when selling 700 units of the

product is

£

700 × 60

100

, that is,£420

Now try the following exercise.

Exercise 206 Further problems on presen-

tation of ungrouped data

1. The number of vehicles passing a stationary
   observer on a road in six ten-minute intervals
   is as shown. Draw a pictogram to represent
   these data.