Cardinal, Ordinal, Interval, and Ratio Scales of Measurement

In data analysis and statistics, understanding how data is measured is essential for selecting appropriate methods of analysis. Data can be categorized into different measurement scales: cardinal, ordinal, interval, and ratio. These scales help determine how variables are quantified and what types of mathematical operations are valid.

Scale of Measurement

1. Cardinal Scale

The cardinal scale refers to numbers that represent quantity. It focuses on the magnitude of numbers without necessarily indicating order or the absolute zero concept. In many contexts, cardinal numbers are synonymous with counting numbers.

These numbers represent the quantity of units sold, making them cardinal numbers used for counting.

Examples:

• 10 employees

• 50 products in stock

• 200 customers visited a store

  
  

2. Ordinal Scale

The ordinal scale represents order or rank of values but does not show the exact difference between ranks. It answers the question "Which position?" but not "how much higher or lower."

The numbers indicate order of preference but not the exact difference in sales between ranks.

Examples:

• 1st, 2nd, and 3rd positions in a competition

• Customer satisfaction ratings (e.g., Very Satisfied, Satisfied, Neutral, Dissatisfied)

• Rankings of brands based on preference

3. Interval Scale

An interval scale not only shows order but also indicates equal differences between values. However, it lacks a true zero point, meaning zero does not imply the absence of the quantity.

Examples:

• Temperature measured in Celsius or Fahrenheit (0°C doesn’t mean "no temperature")

• Calendar years (e.g., 2020, 2021)

• IQ scores

  
  

Table 1: Numerical Example of Interval Scale

Year	Employee Satisfaction Score
2021	70
2022	75
2023	80

The difference between 2021 and 2022 (5 points) is meaningful (see Table 1) , but a score of 0 doesn’t represent the absence of satisfaction, but shows only the absence of an absolute zero.

4. Ratio Scale

A ratio scale includes all the properties of an interval scale, with a meaningful absolute zero, allowing for the comparison of absolute magnitudes and enabling calculations of ratios (e.g., twice as much).

Examples:

• Income (INR 0 means no income)

• Weight (0 kg means no weight)

• Sales revenue

  
  

Table 2: Numerical Example of Ratio Scale (in Business Context)

Branch	Monthly Sales (in INR thousands)
Branch A	100
Branch B	200
Branch C	400

Branch C has twice the sales of Branch B (see Table 2), a comparison possible because the ratio scale has a true zero (0 means no sales).

Table 3: Comparisons among the Scales of Measurement

Scale	Purpose	Mathematical Operations	Example	Zero Meaningful?
Cardinal	Counting quantities	Addition, Counting	50 employees	No
Ordinal	Ranking or ordering	Median, Mode, Rank	1st, 2nd, 3rd place	No
Interval	Measuring differences	Addition, Subtraction	Temperature (°C)	No
Ratio	Measuring absolute values	All mathematical operations	Income (INR), Sales	Yes

Final Thoughts

Understanding the cardinal, ordinal, interval, and ratio scales is crucial for selecting the right analytical techniques. Cardinal numbers count, ordinal numbers rank, interval scales measure differences without an absolute zero, and ratio scales provide full measurement with a meaningful zero. For business decision-making, recognizing the scale of your data ensures accurate analysis and effective strategies.