ABSTRACT
A set is a group of data and an individual value within the set is called a member of the set. Thus, if the masses of five people are measured correct to the nearest 0.1 kilogram 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 themembers is called a population. Some members selected at random from a population are called a sample. 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 the frequency of that member. Thus, in the set {2,3,4,5,4,2,4,7,9},member 4 has a frequency of three, member 2 has a frequency of 2 and the other members have a frequency of one. The relative frequency with 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 frequency of member 5 is 2
9 . Often, relative frequency is
expressed as a percentage and the percentage relative frequency is
(relative frequency× 100)%
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 represented by equally spaced vertical rectangles (see Problem 4).
