WHAT IS CATEGORICAL VARIABLE

A categorical variable is one which describes a particular quality or characteristic. It can be divided into categories. The information collected is called categorical data.

For example,

Getting to school

Example 1 :

Write down the possible categories for the following categorical variables:

a) Gender

b) Favourite football code

c) Hair colour

d) Type of fuel used in a car.

Solution :

(a)  For gender :

(i)  Men  (ii)  Women

(b)  Foot ball code :

American football, Canadian Football, Association Football, Australian Rules Football, Gaelic Football, Rugby Union, Rugby League etc.

(c)  Hair color :

Black, blonde, brown, grey, brunette

(d)  Fuel :

unleaded, premium unleaded, diesel, LPG, super.

Categorical Graphs

Graphs gives us the information to help us to understand the data. For all graphs, it is important to lable the axis.

Two variables under consideration are usually linked by one being independent on the other.

In general, when we draw graphs involving two variables, the independent variable is placed on the horizontal axis  (x-axis) and the dependent variable(y-axis) is placed on the vertical axis.

An exception to this is when we draw a horizontal bar chart.

Acceptable graphs to display categorical data are:

For categorical data, the mode is the category which occurs most frequently. In the graphs above, the mode is the green category.

For each problem below decide if you can display the data as a bar graph, a pie chart, or both. Then create one appropriate graph for the data. Make sure to include a title and all necessary labels. 

Example 2 :

Eye color of Langley AP Statistics students:

Brown  =  64, Blue  =  23, Green  =  36, Other  =  5

Solution :

Example 3 :

Average height of various animals, in cm:

Walaroo  =  105, Eagle  =  88, Tapir  =  97, Zebra  =  146.

Solution :

Example 4 :

55 randomly selected Year 10 students were asked to nominate their favourite subject studied at school. The results of the survey are displayed in the bar chart shown.

a) What are the variables in this investigation?

b) What are the dependent and independent variables?

c) What is the mode?

d) Construct a pie chart for the data. If possible, use a spreadsheet

Solution :

(a)  Favourite subject and frequency.

(b)  Independent variable is subject and dependent variable is frequency.

(c)  Mode is science.

(d)  

Example 5 :

Classify each of the following types of data as categorical or numerical:

a)  weight of Year 8 students

b) brands of coffee

c)  prices of large pizzas

d)  numbers of mobile phones owned by family members

e)  amounts of rainfall in Albion Park

f)  causes of road accidents

g)  sets won in a tennis match

Solution :

a)  weight of Year 8 students

Weight of students will be a numerical value, then it must be a numerical data.

b) brands of coffee

Brands of coffee can be named, then it is categorical data.

c)  prices of large pizzas

Prices of large pizzas must be amount in numerical value. Then it is numerical data.

d)  numbers of mobile phones owned by family members

Number of mobile phones can be mentioned with numerical value, then it is numerical.

e)  amounts of rainfall in Albion Park

Rainfall can be mentioned with numerical value, then it must be numerical.

f)  causes of road accidents

Reasons for road accidents will be in verbal, so it is categorical data.

g) sets won in a tennis match

Sets won can be mentioned with numerical value, then it is numerical data.

Example 6 :

Classify each of the following types of data as categorical, discrete numerical or continuous numerical

a)  people’s eye colours

b)  the amount of time doing exercise

c)  number of points players scored in a netball match

d)  the gender of a newborn baby

e)  people’s ages last birthday

f)  heights of buildings

g)  number of staff employed

Solution :

a)  people’s eye colours

Name of the colours will be verbal, so it is categorical data..

b)  the amount of time doing exercise

The amount of time can be mentioned with numerical value, so the data is numerical continuous.

c)  number of points players scored in a netball match

Number of points must be numerical values, cannot be the decimal. Then it is discrete numerical data.

d)  the gender of a newborn baby

The gender must be name, either boy or girl. So, it is categorical data

e)  people’s ages last birthday

Ages may be a numerical value. So, it is discrete numerical.

f)  heights of buildings

Height of the building must be any number, so it is numerical continuous.

g)  number of staff employed

Number of employees must be numerical values and it must be integers only. So, it must be numerical discrete.

Example 7 :

Here is the bar chart summarizing the 2005 movie genres

a) Which genre was not common?

b) How many people like comedy movie ?

Solution :

a) The least is not common, then thriller or horror is not common.

b) Number of people who like comedy movie is approximately 28.

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