Basic Engineering Mathematics, Fifth Edition

Presentation of statistical data 289

(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.

31.1.2 Further statisticalterminology

Asetis a group of data and an individual value within
the set is called amemberof the set. Thus, if the
masses of five people are measured correct to the near-
est 0.1kilogram and are found to be 53.1kg, 59.4kg,
62.1kg, 77.8kg and 64.4kg then the set of masses in
kilograms for these five people is

{ 53. 1 , 59. 4 , 62. 1 , 77. 8 , 64. 4 }

and one of the members of the set is 59.4
A set containing all the members is called apop-
ulation. Some members selected at random from a
population are called asample. Thus, all car registration
numbers form a populationbut the registration numbers
of, say, 20 cars taken at random throughout the country
are a sample drawn from that population.
The number of times that the value of a member
occurs in a set is called thefrequencyof that mem-
ber. Thus, in the set{ 2 , 3 , 4 , 5 , 4 , 2 , 4 , 7 , 9 },member4
has a frequency of three, member 2 has a frequency of
2 and the other members have a frequency of one.
Therelative frequencywith which any member of a
set occurs is given by the ratio

frequency of member

total frequency of all members

For the set { 2 , 3 , 5 , 4 , 7 , 5 , 6 , 2 , 8 }, the relative fre-

quency of member 5 is

2

9

. Often, relative frequency is

expressed as a percentage and thepercentage relative
frequencyis

(relative frequency× 100 )%

31.2 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 a percent-

age component bar chart. In such a chart, equally

spaced rectangles of any width, but whose height cor-

responds to 100%, are constructed. The rectangles

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 JanuaryFebruaryMarch

Number repaired 11 6 15

Month April May June

Number repaired 9 13 8

Each symbol shown in Figure 31.1 represents two tele-

vision sets repaired. Thus, in January, 5

1

2

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 31.1