Higher Engineering Mathematics, Sixth Edition

530 Higher Engineering Mathematics

(c) The time that a battery lasts ismeasuredand can

have any value between certain limits. Hence these

data arecontinuous.

(d) The amount of money spent on food can only be

expressed correct to the nearest pence, the amount

beingcounted. Hence, these data arediscrete.

Now try the following exercise

Exercise 204 Further problems on discrete

and continuous data

In Problems 1 and 2, state whether data relating to

the topics given are discrete or continuous.

1. (a) The amount of petrol produced daily, for
   each of 31 days, by a refinery.
   (b) The amount of coal produced daily by
   each of 15 miners.
   (c) The number of bottles of milk delivered
   daily by each of 20 milkmen.
   (d) The size of10 samples ofrivets produced
   by a machine.
   [
   (a) continuous (b) continuous
   (c) discrete (d) continuous

]

2. (a) The number of people visiting an exhi-
   bition oneach of 5 days.
   (b) The time taken by each of 12 athletes to
   run 100metres.
   (c) The value of stamps sold in a day by
   each of 20 post offices.
   (d) The number of defective items pro-
   duced in each of 10 one-hour periods
   by a machine.
   [
   (a) discrete (b) continuous
   (c) discrete (d) discrete

]

54.2 Presentation of ungrouped data

Ungrouped data can be presented diagrammatically in

several ways and these include:

(a) pictograms, in which pictorial symbols are used

to represent quantities (see Problem 2),

(b) horizontal bar charts, having data represented

by equally spaced horizontal rectangles (see Prob-

lem 3), and

(c) vertical bar charts, in which data are repre-

sented by equally spaced vertical rectangles (see

Problem 4).

Trends in ungrouped data over equal periods of time

can be presented diagrammatically by apercentage

component bar chart. In such a chart, equally spaced

rectangles of any width, but whose height corresponds

to 100%, are constructed. The rectangles are then sub-

divided into values corresponding to the percentage

relative frequencies of the members (see Problem 5).

Apie diagramis used to show diagrammatically the

parts making up the whole. In a pie diagram, the area of

a circle represents the whole, and the areas of the sectors

of the circle are made proportional to the parts which

make up the whole (see Problem 6).

Problem 2. The number of television sets

repaired in a workshop by a technician in six,

one-month periods is as shown below. Present these

data as a pictogram.

Month Number repaired

January 11

February 6

March 15

April 9

May 13

June 8

Each symbol shown in Fig. 54.1 represents two televi-

sion sets repaired. Thus, in January, 5^12 symbols are used

to represent the 11 sets repaired, in February, 3 symbols

are used to represent the 6 sets repaired, and so on.

January

February

March

Month Number of TV sets repaired ;2 sets

April

May

June

Figure 54.1