Variable Types: The Full Taxonomy

Numerical vs categorical variables in full — discrete, continuous, nominal, ordinal, unstructured data — plus the two classification traps that catch everyone.

4. Variable Types — Full Taxonomy

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                              VARIABLES
                                  |
            +---------------------+---------------------+
            |                                           |
       NUMERICAL                                  CATEGORICAL
      (quantitative)                              (qualitative)
            |                                           |
      +-----+------+                +----------+--------+---------+
      |            |                |          |                  |
  DISCRETE    CONTINUOUS         NOMINAL    BINARY            ORDINAL


        + UNSTRUCTURED DATA (not tabular at all)

4.1 Numerical (Quantitative) Variables

General definition: a variable that takes a number — and specifically a quantifiable number, one you can do meaningful arithmetic on.

Discrete

Takes whole numbers only — 1, 2, 3, 4, 5…

Examples given in class:

Number of cars passing a tollgate every minute — e.g. ~50 vehicles per minute. You cannot have 53.5 cars.
Number of defective items in a box — you cannot have 5.5 defects.
Number of items in a shopping cart

Continuous

Can take any value within a range — infinitely divisible.

Examples given in class:

Amount of rainfall in millimetres (the Chennai rain the night before class)
Spindle speed in rotations per minute — e.g. 333.3 RPM
Motor temperature — e.g. 50.3 °C

4.2 Categorical (Qualitative) Variables

Definition: has two or more levels; cannot be quantified. These are qualitative variables.

Simple examples of categorical values: red / orange / yellow · male / female · low / medium / high.

Nominal

Two or more categories with NO order.

Examples given in class:

Maintenance mode — preventive maintenance / corrective maintenance / predictive maintenance
Material type — steel / aluminium / composite (which material is used to make a part)
Product category on Amazon — laptop / washing machine / refrigerator / bed / shoe
PIN code (see the trap in §5)

Binary

Strictly two categories.

Examples given in class:

Patient has the disease / does not have the disease
Customer churn / no churn
Email spam / non-spam (column name “email type”, values spam or non-spam)
Pass / fail
True / false
Complaint / non-complaint — e.g. whether an application is compliant with government rules
Good / bad
Water / non-water
Cancer / no disease
Flight delayed / not delayed — predicting whether the flight you’re catching will be delayed
Email opened / not opened — for an email campaign
Customer will accept the offer on a call / will not

Business context on the last one: “If you send an email, that is cheaper, that is okay. But if you know whether the customer will accept our offer when you call him — if there’s a possibility he’ll accept, then we’ll call. Otherwise, no. Because talking human to human is very costly.”

This is why binary prediction matters commercially: it lets you allocate expensive resources (human phone calls) only where they’ll pay off.

Ordinal

Categories with a clear order.

Examples given in class:

Education — primary → secondary school → high school → college
Signal quality — no signal → weak → fair → good → strong
Customer service rating — 1 → 2 → 3 → 4 → 5
Customer satisfaction — low → medium → high

“Ordinal data means there is an order in the data. Low, medium, high — there is an order.”

4.3 Unstructured Data

Definition: data not in tabular format — you cannot store it in rows and columns.

Examples:

Raw satellite images with no predefined fields
Images and videos generally

“If your data is not in a tabular format, especially images and videos, we say it is unstructured data. You cannot save them in particular rows and columns.”

5. The Two Classification Traps

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Trap 1 — PIN codes look discrete but are NOT

A PIN code (e.g. 600036, 600042) is written entirely in digits, with no decimal point. It looks exactly like a discrete variable.

The test: can you do meaningful arithmetic on it?

	Cars at a tollgate	PIN code
Values	50 cars, then 52 cars	600036, 600042
Sum	102 cars — meaningful	1200078 — meaningless
Average	51 cars/minute — meaningful	no validity
Difference	meaningful	no meaning
Verdict	Discrete numerical	Nominal categorical

Why nominal specifically? Because on top of failing the arithmetic test, PIN codes also have no order among them.

The rule: “If you can do some arithmetic operations, we’ll say discrete. Non-arithmetic, we’ll say categorical.” “Discrete variables are the quantifiable numbers — you can do some mathematics on them.”

Trap 2 — encoded categories look numerical but are NOT

Databases routinely store gender as 1, 1, 0, 0, 0, 1 rather than as text.

“You should not get confused. You should not think that gender is a numerical variable. It is a categorical variable.”

The encoding is a storage convenience. It does not change the nature of the variable.

6. Classification Quiz — Questions & Answers

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Five in-class questions with the instructor’s confirmed answers.

Q	Item	Answer	Reasoning given
1	PIN code	Nominal (categorical)	Looks discrete, but sum/average/difference produce no valid value, and PIN codes have no order
2	Disease present / not present	Binary	Strictly two categories — “this is present or not”
3	Customer satisfaction rated low / medium / high	Ordinal	There is a clear order in the data
4	Number of items in the shopping cart	Discrete numerical	Whole numbers, arithmetic is meaningful
5	Raw satellite images with no predefined fields	Unstructured data	Cannot be stored in rows and columns

Note: Q1 was the one that generated the most discussion — a student specifically argued “PIN code is fully numeric without any decimal, it can be discrete also, right?”, which triggered the full explanation in §5.