Lecture 1.4 - Introduction and Types of Data - Scales of measurement

Question 1

Scales of measurement

Answer 1

1. Four scales of measurement: nominal, ordinal, interval, ratio.

Question 2

Nominal scale

Answer 2

1. Nominal scale : name categories without implying order.
2. Examples: Name, Board, Gender, Blood group, etc.
3. Sometimes nominal variables might be numerically coded.
4. There is no ordering in the variable.

Question 3

Ordinal scale of measurement

Answer 3

1. Ordinal data represents a measurement scale in which the values have a natural order or ranking but the difference between values is not meaningful.
2. Examples: Ranking of athletes in a race, academic grades (A, B, C), Likert scale responses (strongly agree, agree, neutral, disagree, strongly disagree).
3. Unlike interval and ratio scales, arithmetic operations such as addition, subtraction, multiplication, and division are not valid for ordinal data.

Question 4

Interval scale

Answer 4

I1. f the data have all the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure, then the scale of measurement is interval scale.
2. Interval data are always numeric. We can find out the difference between any two values, but ratios of values have no meaning here because the value of zero is arbitrary.
3. Interval: numerical values that can be added/subtracted.

Question 5

Example of Temperature

Answer 5

1. Nominal variable: response to a question with labels, e.g. “comfortable” or “uncomfortable” for how hot the day is.
2. Ordinal variable: answer with a ranking, e.g. “cold,” “warm,” or “hot” for measuring the temperature of a liquid.
3. Interval variable: numeric values that can be added/subtracted, but ratios have no meaning. E.g. the temperature difference between an AC room set at 20 C and outside at 40 C is 20 C, but it’s incorrect to say outside is twice as hot.

Question 6

Ratio Scale

Answer 6

1. Interval data + Ratio of two values is meaningful = Ratio scale.
2. Examples: Height, weight, age, marks, etc.
3. Ratio scale allows for numerical values that can be added, subtracted, multiplied, or divided.

Question 7

More bifurcation of data

Answer 7

1. Categorical : Nominal and Ordinal
2. Numerical : Interval and Ratio