Representation of Data Statistics: A branch of mathematics dealing with the collection, analysis, interpretation, and meaningful presentation of raw data. Data: Qualitative or quantitative information. datum is singular. data is plural.

Qualitative data: Information about the properties/attributes of data that can only be described without use of numbers. Quantitative data: Information about the properties/attributes of data that can be described with numbers. Variable: The name given to a particular property or attribute of data.

Examples: 1. An ice-cream store sells small, medium and large ice-cream cones. The variable in this case, is size, because it is an attribute of the ice-cream cone that is sold. Size is a qualitative variable because it can only be described in one of three ways: small, medium and large.

Examples: 2. An ice-cream store sells 1 litre, 2 litre and 3 litre ice-cream tubs. The variable in this case, is size, because it is an attribute of the ice-cream tub that is sold. Size is a quantitative variable because it can be described with numbers in one of three ways: 1, 2 and 3 litres respectively. Is ice-cream flavour a qualitative or quantitative variable?

Continuous and discrete variables: The only type of variables that can be continuous or discrete are quantitative variables. Continuous variable example: Consider the weight of students in a class that has a range of 50-70 kilograms. Weight is a continuous variable, because it can take on any value in the range. Discrete variable example: Some students are born with 6 fingers on each hand, while most have 5 fingers on each hand. Number of fingers is a discrete variable, because it can take on only one of two values, that is, 5 or 6.

Stem and leaf diagrams: Stem and leaf diagrams are used to make some sense out of raw data that is usually collected in the form of a list, without any regard to category or other arrangement. Suppose that the flavour of ice-cream is rated from 1 to 100 as follows: 68 34 59 94 34 30 33 37 49 53 18 51 20 40 23 41 46 86 0 74 79 We can arrange this data as follows: 0 | (0) 1 | 8 (1) 2 | 0 3 (2) 3 | 0 3 4 4 7 (5) 4 | 0 1 6 9 (4) 5 | 1 3 9 (3) 6 | 8 (1) 7 | 4 9 (2) 8 | 6 (1) 9 | 4 (1) 6 | 8 means 68. Numbers on left are the stems and numbers on right are the leaves. Numbers in parentheses are the number of leaves belonging to each stem.

Now do Exercise 1A. 