# CATEGORICAL VARIABLE AND NUMERICAL VARIABLE

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.

Examples of categorical variables are :

Getting to school :

The categories could be train, bus, car and walking.

Color of eyes :

The categories could be blue, brown, hazel, green, and grey

What is numerical variable ?

A is one which has a numerical value, and is often called a quantitative variable. The information collected is called numerical data

The weight of year 10 students :

The variable could take any positive value from about 40 kg to 120 kg. Theoretically the variable could take any value on the number line but is very unlikely to take a value outside the range given.

The time taken to get to school :

the variable could take any value from about 1 minute to 80 minutes.

For each of the following variables, indicate whether it is numerical or categorical variable.

Problem 1 :

The time taken to travel to school

Solution :

Time taken can be indicated using numerical values. So, the given data is numerical variable.

Problem 2 :

The number of cousins a person has

Solution :

The number of cousins a person has should be mentioned using numerical value. So, the given data is numerical variable.

Problem 3 :

Voting intention at the next election

Solution :

Voting intention means reason of voting. Every one has types of reasons. So it is categorical variable.

Problem 4 :

The number of cars in a household

Solution :

The number of cars must be represented using numerical value. So, it is numerical variable.

Problem 5 :

The speed of cars on a particular stretch of highway

Solution :

The speed of cars can be represented using numerical value. So, it is numerical variable.

Problem 6 :

Favourite type of apple.

Solution :

Type of apple may have names. So it is categorical variable.

Problem 7 :

Town or city where a person was born

Solution :

Person will born in a place. City will have names. So it is categorical variable.

Problem 8 :

The weight of three-year-old children

Solution :

Weight of three year old children will have different weights. So it is numerical variable.

Problem 9 :

The color of the bottle of wine.

Solution :

It is categorical variable.

Problem 10 :

The number of books a person owns.

Solution :

The number of books must be a numerical value. It is numerical variable.

Problem 11 :

A class of 20 students was asked, how many children are there in your household and the following data was collected ?

1   2   3   3    2    4    5    4    2   3    8    1    2    1   3    2   1  2  1   2

i) What is the variable in this investigation ?

ii)  Is the data discreate or continuous?

Solution :

i)  It is numerical variable.

ii)  It is discrete, because for number of children will not have limit and there is no chance to have decimal value.

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