Chapter 54

Presentation of

statistical data

54.1 Some statistical terminology

Data are obtained largely by two methods:

(a) by counting—for example, the number of stamps

sold by a post office in equal periods of time, and

(b) by measurement—for example, the heights of a
group of people.

When data are obtained by counting and only whole
numbers are possible, the data are calleddiscrete. Mea-
sured data can have any value within certain limits and
are calledcontinuous(see Problem 1).
Asetis a group of data and an individual value within
theset is called amemberof the set. Thus, if the masses
of five people are measured correct to the nearest 0.1kg
and are foundtobe 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 apopulation.

Some members selected at random from a population

are called asample. Thus all car registration numbers

form a population, but 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 member. Thus

in the set:{ 2 , 3 , 4 , 5 , 4 , 2 , 4 , 7 , 9 }, member 4 has a fre-

quency of three, member 2 has a frequency of two 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^29

Often, relative frequency is expressed as a percent-

age and thepercentage relative frequencyis: (relative

frequency× 100 )%.

Problem 1. Data are obtained on the topics given

below. State whether they are discrete or continuous

data.

(a) The number of days on which rain falls in a

month for each month of the year.

(b) The mileage travelled by each of a number of

salesmen.

(c) The time that each of a batch of similar

batteries lasts.

(d) The amount of money spent byeach of

several families on food.

(a) The number of days on which rain falls in a given

month must be an integer value and is obtained by

countingthe number of days. Hence, these data

arediscrete.

(b) A salesman can travel any number of miles (and

parts of a mile) between certain limits and these

dataaremeasured.Hence thedataarecontinuous.