Measurement meaning determines valid arithmetic
A number can be a measurement, a label, or an ordered response. Its meaning decides which calculations make sense.
| Type | Examples | Meaningful operations |
|---|---|---|
| Nominal category | Programme, study mode | Counts, proportions, mode; no intrinsic order or mean |
| Ordinal category | Satisfaction 1-5; low/medium/high workload | Order, category distribution, median under an appropriate convention; equal gaps are not guaranteed |
| Discrete numerical | Number of logins, submissions | Numerical summaries when the counts have the stated meaning |
| Continuous numerical | Duration, measured score on a sufficiently fine scale | Numerical summaries with units and a suitable interpretation |
| Identifier | Student ID | Match, check uniqueness, count distinct; arithmetic averages have no useful interpretation |
The slides treat scores as numerical measurements. A score recorded only as whole points is technically discrete; the important exam distinction is a quantitative measurement versus an arbitrary category code. Its stored Python type does not settle its meaning.
Keep identifiers as text to preserve leading zeros. A numeric-looking programme code does not become a meaningful measurement. Satisfaction means can be reported with an explicit equal-step convention, but show category frequencies too; an average can conceal polarisation.
Sources: W1 PDF pp. 3, 13-17, 22-30, 32-53, 57-60; L1 Parts 1-5.
The lecture defines a row and an identifier. Here you check that students has one row per person and choose the matching table.
The lecture's summary context becomes a denominator check: all student rows for a response rate, recorded ratings for an observed mean.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
How should student ID 00101 be stored?
Satisfaction categories 1–5 are best described as what?
2. Application
Apply the concept to a case or calculation.
Which summary is appropriate for programme names?
Number of submitted assignments is what kind of variable?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Converting ID '00101' to an integer mainly risks what?
Which claim is unsupported solely by rating codes 2 and 4?
Explain it in writing
Self-checked, not marked. Write a few sentences, then compare with the example answer. Your writing is saved as you type.
Show an example answer
The codes name categories. Changing which programme is called 1 changes the mean without changing any real programme information. Counts or proportions are meaningful instead.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
Yes, if the equal-step numerical treatment is stated and suitable for the task. Also show category frequencies, because the same mean can hide very different response patterns.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?