Nominal, Ordinal, Interval

Section 01

The Story That Makes It Click

You are a data scientist at a delivery company. Your boss drops four spreadsheets on your desk and says: "Find the average for each of these."

Spreadsheet	Column	Sample values
A	Driver region	North, South, East, West, North, East
B	Customer satisfaction	Very Happy, Happy, Neutral, Unhappy, Very Happy
C	Outside temperature at delivery	−5°C, 0°C, 12°C, 18°C, 25°C
D	Package weight	0.5 kg, 1.2 kg, 4.8 kg, 0.3 kg, 12.0 kg

You open Python and type df.mean() on all four. Spreadsheet D gives a sensible answer — 3.76 kg. The rest either error or produce nonsense. What went wrong?

⚠️

You cannot average "North, South, East, West"

The mean of North and South is not "East." The average satisfaction between "Very Happy" and "Unhappy" is not necessarily "Neutral." And whether −5°C is "half as cold" as 10°C depends on which scale you use. Data type determines which operations are mathematically valid. Using the wrong statistic on the wrong data type produces numbers that look precise but mean nothing.

In 1946, psychologist Stanley Stevens published a landmark paper defining four levels of measurement — also called data types — that answer exactly this question: what can you legitimately do with this data?

Section 02

The Four Types — Overview

The four types form a hierarchy. Each level inherits the properties of all levels below it and adds one more. As you move up the hierarchy, the data becomes more informative and more statistics become valid.

📊 The Hierarchy of Data Types

Nominal

Named categories. No order, no numbers, no gaps. Only tells you which group something belongs to.
Property added: Identity — values have names that distinguish them.

Ordinal

Ordered categories. You know which is bigger or better, but not by how much.
Property added: Order — values can be ranked meaningfully.

Interval

Ordered with equal gaps. The difference between values is meaningful, but zero is arbitrary.
Property added: Equal intervals — the distance between any two adjacent values is the same.

Ratio

Ordered, equal gaps, and true zero. All arithmetic is valid. Zero means "none of it."
Property added: True zero — zero means complete absence of the quantity.

Type	Has identity?	Has order?	Equal gaps?	True zero?
Nominal	Yes	No	No	No
Ordinal	Yes	Yes	No	No
Interval	Yes	Yes	Yes	No
Ratio	Yes	Yes	Yes	Yes

Section 03

Nominal Data — Just Names

Nominal data is the simplest type. Values are labels or categories with no natural order. You can count how many are in each category, but you cannot rank them or do arithmetic.

The story — sorting the post room

A post room worker sorts 200 parcels into four regions: North, South, East, West. She counts: 62 North, 48 South, 55 East, 35 West. The mode is North — the most common destination. That is the only statistic that makes sense here.

If someone asks "what is the average region?" the question is meaningless. If someone asks "is North bigger than South?" they mean count, not value. North is not a bigger number than South — it is just a different label.

Valid stats

✅

Mode (most common)
Frequency counts
Percentages
Chi-square test

Invalid stats

❌

Mean (no average label)
Median (no order)
Standard deviation
Any arithmetic

Real examples

🏷️

Blood type: A, B, AB, O
Eye colour
Programming language
Country, city, postcode

Situation	Nominal column	Correct question to ask
Customer database	Gender	Which gender is most common in our users?
Hospital records	Blood type	What percentage of patients are blood type O?
E-commerce orders	Payment method	Is credit card or PayPal used more often?
Job applications	Degree subject	What is the most common degree among applicants?
App analytics	Device type	What share of users are on iOS vs Android?

💡

Nominal data encoded as numbers is still nominal

Many datasets encode nominal categories as integers — 1 = Male, 2 = Female, 3 = Non-binary, or 1 = North, 2 = South, 3 = East, 4 = West. The numbers are just shorthand labels. The average of (1 + 3) / 2 = 2 does not mean "Female." Always check what encoded numbers represent before applying any arithmetic to them.

Section 04

Ordinal Data — Order Without Equal Gaps

Ordinal data has a meaningful order — you know which value is higher or lower. But the gaps between values are not necessarily equal. You cannot say the difference between rank 1 and rank 2 is the same as the difference between rank 4 and rank 5.

The story — the restaurant table

Four friends eat at a restaurant and each rates their experience: Alice gives 5 stars, Bob gives 4 stars, Carol gives 2 stars, Dan gives 5 stars. You know Alice enjoyed it more than Carol. You know 5 stars is better than 4 stars. But is the gap between 4 and 5 the same emotional distance as the gap between 1 and 2?

Not necessarily. The jump from "Terrible" to "Bad" might represent far more improvement in experience than the jump from "Good" to "Excellent." The numbers create an illusion of precision that does not really exist. This is why the median, not the mean, is the correct measure of centre for ordinal data.

🧮 Why the mean misleads on ordinal data

Scenario

Ten customers rate a product on a 1–5 scale:
[5, 5, 5, 5, 5, 1, 1, 1, 1, 1]
Five absolutely love it. Five absolutely hate it.

Mean

(5+5+5+5+5+1+1+1+1+1) / 10 = 30 / 10 = 3.0
Interpretation: "Average satisfaction — customers are neutral." This is completely wrong. Nobody rated it 3. Nobody is neutral.

Median

Sorted: [1, 1, 1, 1, 1, 5, 5, 5, 5, 5]
Median = average of 5th and 6th values = (1+5)/2 = 3.0
Same number — still misleading. This is why for ordinal data you must always look at the full distribution, not just a single central value.

Correct approach

Report the frequency of each rating:
⭐⭐⭐⭐⭐ = 50% ⭐⭐⭐⭐ = 0% ⭐⭐⭐ = 0% ⭐⭐ = 0% ⭐ = 50%
Bimodal distribution revealed. This product divides opinion completely. That is the real story.