Higher Engineering Mathematics

Statistics and probability

J

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.

Measured data can have any value within certain

limits and are calledcontinuous(see Problem 1).

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

nearest 0.1 kg and are found to be 53.1 kg, 59.4 kg,

62.1 kg, 77.8 kg and 64.4 kg, 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 a sample. Thus all car

registration numbers form a population, but the reg-

istration 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}, member

4 has a frequency of three, member 2 has a fre-

quency 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^29.

Often, relative frequency is expressed as a per-

centage 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 by each 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

bycountingthe 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 data aremeasured. Hence the data are

continuous.

(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 are

discrete.

Now try the following exercise.

Exercise 205 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.