Nominal vs Ordinal
People use numbers for different purposes. Ancient people needed numbers to count their belongings. So they invented counting numbers. As technology developed, the human needs became complex, and they needed different identifications for different objects. The number systems were developed or modified according to their needs.
In statistics, different type of numbers such as ‘Nominal’ and ‘Ordinal’ are used to determine the type of statistic that is used. These terms were widely used before; however, they have begun to fall out of favor.
Natural numbers are used for two proposes. One is to count the number of elements in a set. Other is to define the position of an object in an order or a set. Ordinal number is an extension of natural numbers. We use ordinal numbers to indicate the position or the rank of an object placed in an order. Ordinary numbers do not represent any quantity. For example, in “apple, orange, banana” the second word is “orange”.
Georg Cantor introduced ordinal numbers in 1870. He introduced these numbers to categorize sets with certain order in the structures, and accommodate infinite sequences. Ordinary numbers are applicable on arithmetic operations such as addition, subtraction, multiplication and division.
The name nominal comes from the Latin ‘nomen’, which means ‘name’. A nominal number is a number used as a name for identification. Ordinal numbers do not represent any quantity or a rank. Therefore, they are numbers with no other information except identification for objects. It does not have to be defined on a set of objects. Nominal items may have a number assigned to them. Nominal item can be any object which is vital in everyday life.
In mathematics, nominal numbering is defined as a one-to-one function between a set of numerals and a set of objects. Therefore, each item has a unique identification assign to them. No two items carry a common identity. ZIP codes, telephone numbers and driver’s license numbers are few common examples for nominal numbers.
Arithmetic operations such as addition, subtraction, multiplication and division have no meaning on nominal numbers. However, comparison of two nominal numbers is a meaningful operation on nominal numbers.
What is the difference between Nominal and Ordinal Numbers?
• Ordinary numbers indicate the position of an object, while nominal numbers indicate identification of an object.
• Ordinary numbers are defined on a set of objects, which are ordered. The order is not essential for nominal numbers.
• Ordinal numbers can be used in arithmetic operations, while nominal numbers have no meaning in arithmetic operations.