Question

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.

(a) The birth state of each student in class

Answer 1

Level of mesurements in Statistics:-

Nominal, Ordinal, Interval, and Ratio are defined as the four fundamental levels of measurement scales that are used to capture data in the form of surveys and questionnaires, each being a multiple choice question.

Nominal Scale:-

Nominal Scale, also called the categorical variable scale, is defined as a scale used for labeling variables into distinct classifications and doesn’t involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Nominal scale is a naming scale, where variables are simply “named” or labeled, with no specific order.

Examples-

City, Town, Country, Gender, Political prefrences, Place of residence etc

Ordinal Scale:-

Ordinal Scale is defined as a variable measurement scale used to simply depict the order of variables and not the difference between each of the variables. These scales are generally used to depict non-mathematical ideas such as frequency, satisfaction, happiness, a degree of pain, etc. It is quite straightforward to remember the implementation of this scale as ‘Ordinal’ sounds similar to ‘Order’, which is exactly the purpose of this scale.

Example:-

How satisfied are you with our services?

• Very Unsatisfied – 1
• Unsatisfied – 2
• Neutral – 3
• Satisfied – 4
• Very Satisfied – 5

Interval Scale:-

Interval Scale is defined as a numerical scale where the order of the variables is known as well as the difference between these variables. Variables that have familiar, constant, and computable differences are classified using the Interval scale. It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving.

Interval Scale Examples

• There are situations where attitude scales are considered to be interval scales.
• Apart from the temperature scale, time is also a very common example of an interval scale as the values are already established, constant, and measurable.
• Calendar years and time also fall under this category of measurement scales.
• Likert scale, Net Promoter Score, Semantic Differential Scale, Bipolar Matrix Table, etc. are the most-used interval scale examples.

Ratio Scale:-

Ratio Scale is defined as a variable measurement scale that not only produces the order of variables but also makes the difference between variables known along with information on the value of true zero. It is calculated by assuming that the variables have an option for zero, the difference between the two variables is the same and there is a specific order between the options.

Ratio Scale Examples

The following questions fall under the Ratio Scale category:

• What is your daughter’s current height?
  • Less than 5 feet.
  • 5 feet 1 inch – 5 feet 5 inches
  • 5 feet 6 inches- 6 feet
  • More than 6 feet
• What is your weight in kilograms?
  • Less than 50 kilograms
  • 51- 70 kilograms
  • 71- 90 kilograms
  • 91-110 kilograms
  • More than 110 kilograms

Answer:-

(a) The birth state of each student in class is a place which may be a city or town etc. Hence appropriate level of measurement is Nominal Scale.