L1.4: Introduction and Types of Data - Scales of Measurement

​

Learning outcomes

• define the four scales of measurement
• identify whether a variable is nominal, ordinal, interval, or ratio
• explain the role of order, equal gaps, and true zero
• solve scale-of-measurement MCQs correctly

​

Why scales matter

• The scale tells us what kind of comparison is meaningful.
• It affects:
  • ordering
  • difference interpretation
  • ratio interpretation
  • allowed summaries and analysis

​

1. Nominal scale

• Labels only
• No order
• Numbers, if present, are just category codes

• blood group
• religion
• department code

​

2. Ordinal scale

• Categories have order
• Gaps between levels are not guaranteed equal

• class rank
• satisfaction level
• letter grade categories in broad grouping

​

3. Interval scale

• Ordered values
• Equal intervals between values
• No true zero

• temperature in Celsius
• temperature in Fahrenheit

• 0°C does not mean complete absence of temperature.

• 20°C is not “twice as hot” as 10°C.

​

4. Ratio scale

• Ordered values
• Equal intervals
• True zero exists

• height
• weight
• age
• income
• number of books

• 0 kg means no weight of the measured amount
• ratios are meaningful

​

Quick comparison table

​

How to solve scale questions

1. Is it only a label?
2. If not, is there a natural order?
3. If yes, are the intervals equal?
4. If yes, is zero a true absence?

​

Exam hints and traps

• Rank has order but not equal measured gaps, so it is ordinal.
• Celsius has equal gaps but no true zero, so it is interval.
• Height and weight have meaningful zero, so they are ratio.
• Category codes like 1, 2, 3 are not interval just because numbers are used.

​

Quick practice

1. blood group
2. rank in race
3. temperature in Celsius
4. monthly income
5. pain level classified as mild / moderate / severe

​

Answer key

1. nominal
2. ordinal
3. interval
4. ratio
5. ordinal