Higher Engineering Mathematics

528 STATISTICS AND PROBABILITY

(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 of 10 samples of rivets produced

by a machine.

[

(a) continuous (b) continuous

(c) discrete (d) continuous

]

2. (a) The number of people visiting an exhibi-
   tion on each of 5 days.

(b) The time taken by each of 12 athletes to

run 100 metres.

(c) The value of stamps sold in a day by each

of 20 post offices.

(d) The number of defective items produced

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
Problem 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 apercent-
age component bar chart. In such a chart, equally
spaced rectangles of any width, but whose height
corresponds to 100%, are constructed. The rectan-
gles are then subdivided 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 tele-

vision 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.

Figure 54.1

Problem 3. The distance in miles travelled by

four salesmen in a week are as shown below.

Salesmen P Q R S

Distance travelled

(miles) 413 264 597 143

Use a horizontal bar chart to represent these data

diagrammatically.

Equally spaced horizontal rectangles of any width,

but whose length is proportional to the distance trav-

elled, are used. Thus, the length of the rectangle

for salesmanPis proportional to 413 miles, and so

on. The horizontal bar chart depicting these data is

shown in Fig. 54.2.