Data is everywhere and increasingly drives many aspects of our day-to-day lives. Here we explain the different types of data that can be collected and some ways of illustrating this data.
Definitions
\(\mathbf{Population}\): the total group of individuals or items under consideration.
\(\mathbf{Sample}\): a group of individuals or items chosen from the population.
\(\mathbf{Data}\): the information collected from the sample or population.
\(\mathbf{Statistic}\): a number calculated from the sample data.
\(\mathbf{Parameter}\): a number calculated from the population data.
Types of data
Data may be either qualitative (categorical) or quantitative (numerical)
\(\mathbf{Qualitative\,Data}\) (classified or labeled).
Data is put into non-numerical categories. Blood type, religion, cause of death, are all examples of qualitative data.
\(\mathbf{Quantitative\,Data}\) (counted or measured).
There are two types of quantitative data.
\(\mathit{Discrete\,Data:}\) data is put into categories depending on its counted number; for example, the number of children in a family.
\(\mathit{Continuous\,Data:}\) data is put into categories depending on its measured size; for example, height.
Graphical representation of data
Qualitative/Categorical data is often represented by means of a bar chart or a pie chart.
Quantitative/Numerical Data is often represented by means of a frequency bar chart called a histogram.
Examples
The table shows the percentage of Australian imports from various countries. This data can be represented on a pie chart so that comparisons are easier.
Country
Imports %
China
22
Japan
20
South Korea
8
India
8
USA
5
UK
4
New Zealand
4
Others
29
A group of school students were surveyed to find the number of children in their families. This data can be represented using a histogram.
No. of Children
Frequency
1
13
2
21
3
11
4
4
5
3
6
1
7
1
Total
54
Exercise 1
Label each of the following as either a categorical or numerical variable. For the numerical variables label each as either discrete or continuous.
Hair colour
A persons religion
A persons height
Number of children in a family
The weights of babies born on a particular day
The number of crimes committed in Victoria each week
The distance traveled to work by the employees of a large company
The make of car driven by students at RMIT
Categorical
Categorical
Numerical – continuous
Numerical – discrete
Numerical – continuous
Numerical – discrete
Numerical – continuous
Categorical
Exercise 2
Represent the data in example 1 in a bar graph.
Exercise 3
A group of employees recorded the time that it took them to travel to work on a particular day (see table below). Represent this data using a histogram.
