Difference among Cardinal, Ordinal, and Nominal Numbers

Cardinal Numbers, Ordinal Numbers, and Nominal Numbers

What is a Cardinal Number?

Cardinal numbers are the numbers that are used to count or measure the amount of something such as the number of objects in a set, the size of a group, or the quantity of substance. These numbers are also called counting numbers.

1. It answers the question “How many”.

2. It doesn’t have any value as fractions or decimals.

3. Statistical tests like T-test and ANOVA are used to analyze the nominal data.

Example:  If there are 12 people playing cricket, then the corresponding cardinal number to represent the number of players is 12.

Note: The cardinality of a group or a set is defined as the total number of elements in that group or set.

Example: A = {apple, banana, mango, orange}

The cardinality of A is 4.

What is an Ordinal Number?

Ordinal numbers classify variables that have a natural order or rank, in simple terms ordinal number represents a position or order in a sequence. It is used to indicate the ranking or order of items or events based on their position relative to each other.

1. It can be represented in tabular or graphical format.

2. Statistical Tests like Spearman rho correlation, mood’s median test, etc, are used to analyze data.

Example:

1. Education: 12^th, Graduate, Post-Graduate, Doctoral, and Post-Doctoral

2. Income Group: Low, Medium, and High

3. Rating: Excellent, Very Good, Good, Bad, Worst.

What is a Nominal Number?

The term ‘nominal’ comes from the Latin word ‘nomen’ or ‘nominalis’ which means name. Nominal numbers are the types of numbers that represent a name or label for a category. It is used to group or classify items based on their shared characteristics or attributes.

1. It divides variables into mutually exclusive and labelled categories.

2. Statistical Tests like chi-square goodness of fit and chi-square test of independence are used to analyze nominal data.

Example:

1. Favourite Colours: ‘red’, ‘blue’, ‘green’, ‘yellow’.

2. Different types of cars: ‘SUV’, ‘sedan’.

3. Blood Type: ‘A’, ‘B’, “AB”, ‘O’.

4. Marital Status: ‘Single’, ‘Married’, ‘Divorced.’

Difference among Cardinal, Ordinal, and Nominal

1. Meaning:

(i). Cardinal number represents quantity.

(ii). Ordinal number represents position or order.

(iii). Nominal number represents categories and labels.

2. Properties:

(i). Arithmetic operations can be performed on cardinal numbers.

(ii). Arithmetic operations can’t be performed on ordinal as well as on nominal data, but ordinal values can be compared.

3. Representation:

(i). Cardinal numbers are represented by numerals (or digits)

(ii). Ordinal numbers are represented by the combination of numbers or words (1^st, 2^nd, 3^rd), whereas nominal numbers are represented by words or symbols (that indicate category or label).

4. Comparison:

(i). Cardinal numbers can be compared using operators such as (<, >, <=, >=).

(ii). Ordinal numbers can be compared but not for magnitude, whereas nominal numbers can’t be compared for either magnitude or order.

5. Level of Measurement:

(i). Cardinal numbers are used in fields such as mathematics, physics, and finance.

(ii). Ordinal numbers are used in the field such as ranking, sports, and surveys.

(iii). Nominal numbers are used in the field such as categorization, labelling, and data analysis.