SCALES OF
MEASUREMENT
Dr. Ajay Kumar Koli, PhD | SARA Institute of Data Science, India
Scales of Measurement:
The scales of measurement are a way to classify data based on their attributes and the mathematical operations that can be performed on them.
Scales of Measurement:
They are classified into four types:
Nominal scale.
Ordinal scale.
Interval scale.
Ratio scale.
Nominal Scale
Categorizes data without any order or rank.
Nominal Scale Examples
| Variable | Example Values |
|---|---|
| Gender | Male, Female, Non-binary |
| Religion | Hindu, Muslim, Christian, Sikh, Buddhist |
| Marital Status | Single, Married, Divorced, Widowed |
| Political Party | BJP, Congress, AAP, CPI |
| Blood Type | A, B, AB, O |
| Nationality | Indian, German, Australian, Argentinian |
| Color Names | Red, Blue, Green, Yellow |
| Types of Transport | Bus, Train, Bicycle, Car |
| Academic Discipline | Sociology, Physics, History, Economics |
Ordinal Scale
Data with a meaningful order but unequal intervals.
Ordinal Scale Examples
| Variable | Example Values | Notes |
|---|---|---|
| Education Level | Primary < Secondary < Graduate < Postgraduate | Rank exists, but interval not equal |
| Socioeconomic Status | Low < Middle < High | Ordered categories |
| Agreement Level | Strongly Disagree < Disagree < Neutral < Agree < Strongly Agree | Likert scale |
| Customer Satisfaction | Very Unsatisfied < Unsatisfied < Neutral < Satisfied < Very Satisfied | Common in surveys |
| Military Ranks | Captain < Major < Colonel | Hierarchical but no fixed interval |
| Class Position | First < Second < Third | Ranks exist, differences unknown |
| Pain Level (self-reported) | No pain < Mild < Moderate < Severe | Ordered, subjective |
Interval Scale
Ordered data with equal intervals but no true zero point.
Interval Scale Examples
| Variable | Explanation |
|---|---|
| Temperature in °C or °F | The difference between 20°C and 30°C is the same as between 30°C and 40°C, but 0°C ≠ no temperature. |
| IQ Scores | An IQ of 120 is 20 points more than 100, but not “twice as intelligent” as someone with 60. |
| Calendar Years | 2020 and 2025 are 5 years apart, but 0 AD is not the start of time. |
| Time of Day (on a 12-hr or 24-hr clock) | 6 PM is 3 hours after 3 PM, but 0:00 (midnight) is not a true zero. |
| Standardized Test Scores | E.g., SAT or GRE scores — differences are meaningful, but zero doesn’t mean “no knowledge.” |
Ratio Scale
Ordered data with equal intervals and a true zero point.
Ratio Scale Examples
| Variable | Example Values | True Zero? | Notes |
|---|---|---|---|
| Height | 160 cm, 170 cm, 180 cm | Yes | 0 cm = no height |
| Weight | 50 kg, 70 kg, 0 kg | Yes | You can say 70 kg is twice as heavy as 35 kg |
| Income | ₹0, ₹10,000, ₹50,000 | Yes | 0 = no income |
| Age | 0 years, 25 years, 50 years | Yes | 0 = no age |
| Distance | 0 km, 5 km, 10 km | Yes | 0 = no distance |
| Duration (time) | 0 minutes, 30 minutes, 1 hour | Yes | 0 = no time elapsed |
| Number of Children | 0, 1, 2, 3 | Yes | 0 = no children |
| Calories consumed | 0 kcal, 500 kcal, 2000 kcal | Yes | 0 = no calories |
| Marks or Scores (raw) | 0 to 100 | Yes | 0 = no correct answers |
