Scales of Measurement: Types, Examples, and Uses

Scales of measurement is an important topic in mathematics and statistics as it helps us to understand and organize data properly. A scale of measurement tells us how a number or value is used to represent information. Using these scales, we can easily compare, arrange, and analyze data.

There are mainly four types of scales of measurement: nominal, ordinal, interval, and ratio. Each scale has its meaning and use. For example, the nominal scale is used for names or labels (e.g., color, students names), the ordinal scale shows order or ranking (e.g., 1, 2, 3); the interval scale shows the same difference (e.g., the temperature in Celsius); and the ratio shows the value with a real zero point (e.g., weight, height, age).

In this article, we will learn about each type of measurement, their use, differences, and examples of real life. By the end, you will understand how the data can be measured in different ways, which will make troubleshooting and making the information much easier.

 

Table of Content

 

• What is a Scale?

• What are Scales of Measurement?

• Nominal Scale

• Ordinal Scale

• Interval Scale

• Ratio Scale

• The Hierarchy of Measurement Scales

What is a Scale?

A scale is a tool or method used to measure or compare things, and it tells us how long, big, hot, heavy something is. In simple terms, a scale provides us with numbers or units to better understand objects and events.

Example:

• Ruler: Length in cm

• Weighing scale: Weight in kg

• Thermometer: Temperature in °C

What are Scales of Measurement?

A scale of measurement (also called a level of measurement) is a classification that describes the nature of information contained within values assigned to variables.

In simpler terms, it is a system that tells us how much information a number or category actually carries.

Consider the following examples:

• The number 7 on a football jersey: It is just a label. It does not mean the player is ‘7 times better’ than player #1.

• The number 7 on a pain scale (0–10): It indicates more pain than 5 and less than 9, but the gaps are not necessarily equal.

• The number 7°C on a thermometer: The difference between 7°C and 14°C is exactly the same as between 14°C and 21°C, but 14°C is not "twice as warm" as 7°C.

 

 

Nominal Scale

The nominal scale is the first level of measurement. It simply categorises or labels variables without any quantitative value or order attached. They are simply tags to identify. 

Numbers on a nominal scale are nothing more than codes or tags. You can count how many fall in each category, but you cannot order them, add them, subtract them, or compare their sizes.

Formal Definition: A nominal scale classifies data into mutually exclusive, exhaustive categories where the categories have no inherent rank or order. The only mathematical operation permitted is counting (and finding the mode).

Characteristics of Nominal Scale:

• It divides things into two or more groups or categories. Data is sorted into categories, nothing more.

• It is qualitative (about names, not numbers).

• The numbers are only for naming or counting, not for showing size or order.

• No arithmetic: You cannot calculate mean, median, or standard deviation from nominal data.

• Mutually exclusive: Each observation belongs to one and only one category.

Examples: 

1. Gender

Categories: Male, Female, Non-binary, Prefer not to say. There is no meaningful order here. Female is not ‘greater than’ Male.

2. Blood Type

Categories: A, B, AB, O. These are labels for biological categories. AB is not mathematically larger than A.

3. Eye Colour

Categories: Brown, Blue, Green, Hazel, Grey. Purely descriptive. No ranking exists.

Ordinal Scale

An ordinal scale is the second level of measurement. An ordinal scale goes one step beyond nominal by adding the ability to rank or order categories. It is used to arrange the data in order or rank. The ordinal word comes from ‘order’. So, that ordinal data means data that can be grouped, named, and ranked.

Formal Definition: An ordinal scale classifies data into categories that can be meaningfully arranged in a ranked order, but where the differences between adjacent categories are unknown or unequal.

Characteristics of Ordinal Scale:

• Ordered categories: It shows the order or ranking of items.

• It tells us which is greater or smaller, but not how much greater.

• It gives more information than the nominal scale because it not only names things but also puts them in order.

• Unknown intervals: The gap between Rank 1 and Rank 2 may be different from the gap between Rank 2 and Rank 3.

• It is useful in surveys & studies where people give their choices in order. Non-parametric statistics are typically used.

Examples

1. Academic Ranks / Class Standings

1st, 2nd, 3rd in class. We know who performed best, but we do not know by how much. The gap between 1st and 2nd place may be vastly different from the gap between 2nd and 3rd.

2. Customer Satisfaction Surveys

Very Dissatisfied → Dissatisfied → Neutral → Satisfied → Very Satisfied. There is a clear order, but is the gap between ‘Dissatisfied’ and ‘Neutral’ not necessarily same as between ‘Satisfied’ and ‘Very Satisfied’.

3. Likert Scale Responses

Strongly Disagree → Disagree → Neutral → Agree → Strongly Agree. Widely used in research, but technically ordinal. The jump from ‘Disagree’ to ‘Neutral’ may not equal the jump from ‘Agree’ to ‘Strongly Agree’.

4. Socioeconomic Status

Low income → Middle income → High income. Clearly ordered, but the income gap between ‘low’ and ‘middle’ varies dramatically by context.

Interval Scale

The interval scale is the third level of measurement in statistics. Here, not only are the values ordered, but the differences (intervals) between values are equal and meaningful. 

Formal Definition: An interval scale is a quantitative measurement scale with ordered categories and equal intervals between consecutive values, but without an absolute zero point. Addition and subtraction are valid; multiplication and division are not.

Characteristics of Interval Scale:

• Equal intervals: The difference between any two adjacent points is exactly the same throughout the scale.

• It is Quantitative, meaning we can use numbers.

• We can add and subtract values to find differences.

• We can calculate the mean, median.

• No true zero: The 0 is not absolute; it just acts as a point.

• Negative values are possible.

Examples: 

1. Temperature in Celsius and Fahrenheit

Classic interval scale. Differences are meaningful; ratios are not.

2. Calendar Dates

The year 2000 AD is not ‘twice as recent’ as the year 1000 AD. The year 0 AD is not a true absence of time.

3. IQ Scores

An IQ of 120 is not ‘20% more intelligent’ than an IQ of 100. The intervals are equal, but there is no absolute zero intelligence.

5. Credit Scores (300–850)

Equal intervals exist within the range, but a score of 600 is not ‘twice as creditworthy’ as 300.

Ratio Scale

The ratio scale is the Fourth level of measurement in statistics. It is the highest and most informative level of measurement. It has all the properties of the interval scale, plus one crucial addition: an absolute zero point. A true zero means a complete absence of the attribute being measured.

Formal Definition: A ratio scale is a quantitative measurement scale with equal intervals between values and a true zero point representing the complete absence of the measured attribute, making all arithmetic operations meaningful.

Characteristics of Ratio Scale:

• True zero: It has a true zero. 

• Equal intervals: Same as interval scale.

• It never has negative numbers because 0 means nothing.

• All arithmetic operations valid: With this scale, we can do all kinds of math: +, -, *, %

• We can find the mean, median, and mode using data on this scale.

• It also allows unit conversions.

• Ratio statements are meaningful: "A is twice as large as B" has genuine mathematical meaning.

Examples: 

1. Weight (kg or lbs)

0 kg means no weight. 80 kg is genuinely twice the weight of 40 kg. 

2. Height (cm or inches)

A person 180 cm tall is genuinely 1.5 times taller than someone who is 120 cm. Zero height = no height.

3. Age (in years)

Age 30 is twice as old as age 15. Age 0 means just born (no life lived yet).

4. Distance / Length

10 km is exactly twice as far as 5 km.

The Hierarchy of Measurement Scales

The four scales form a clear hierarchy.

RATIO          ← Most information (true zero + equal intervals + order + labels)

   ↑

INTERVAL       ← Equal intervals + order + labels

   ↑

ORDINAL        ← Order + labels

   ↑

NOMINAL        ← Labels only (least information)

The scales of measurement help us to understand, compare, and organize data correctly. Each scale has its purpose. The nominal scale is for naming or labeling, the ordinal scale is to organize in order, the interval scale is to show equal gaps between the values, and the ratio scale is for numbers with a true zero.

By learning these scales, we can measure things such as names, ranking, temperature, height, weight, time, and more. These scales make it easy to study data, solve problems, and explain the situation in real life in a simple way.

 

Frequently Asked Questions on Scales of Measurement

1. What are the 4 scales of measurement?

Answer: The four scales of measurement are nominal, ordinal, interval, and ratio. These scales categorize data based on the nature of the information they contain and the mathematical operations that can be meaningfully applied to them.

2. What are the scales and their types?

Answer: There are 4 types of scales, based on the extent to which scale values have the arithmetic properties of real numbers. The arithmetic properties are order, equal intervals, and a true zero point. From the least to the most mathematical, the scale types are nominal, ordinal, interval, and ratio.

3. What are the three types of measurement?

Answer: The three measures are descriptive, diagnostic, and predictive. Descriptive is the most basic form of measurement. A Klout score, your Google Pagerank, and the number of unique visitors to your website. Descriptive measurements are what most of us believe measurements to be.

4. What are some types of scales?

Answer: Some important scale types include major, minor, pentatonic, chromatic, whole tone, and blues scales.

5. What are the three types of weighing scales?

Answer: Types of Weighing Scales Based on Use

• Mechanical Weighing Scales.

• Digital Weighing Scales.

• Analytical Weighing Scales