The summary contract
An average is only useful if the reader knows what was averaged and how many measurements were available.
Before calculating, state the observational unit, measurement unit, target population, valid n, missing count and distribution shape. Then choose a centre and spread suited to the question. A summary compresses data: it necessarily omits individuals, tails, modes, groups and collection context. Say which omission matters to the decision.
len(x) counts entries including missing ones; x.count() counts observed values; x.mean() normally ignores missing values. A mean from 916 respondents is not automatically the mean for all 1,200 invited students. The W2 lecture example has 284 missing responses, about 23.7%.
Sources: W2 PDF pp. 2-60; L2 Sections 1-8. The personalised Lab 2 has 240 synthetic students, unlike the 1,200-student lecture dataset. Do not mix their numbers.
The lecture's summary context becomes a denominator check: all student rows for a response rate, recorded ratings for an observed mean.
The lecture's question-first approach decides which summary to use: a typical student and total observed workload are different requests.
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.
What should accompany an observed mean?
There are 1,200 invitees and 916 ratings. What is the mean's valid n?
2. Application
Apply the concept to a case or calculation.
Values are [5,7,missing]. What n is used by the observed mean?
Which report gives an interpretable centre?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Out of 240 invited students, 195 rate satisfaction. How many ratings are missing?
An observed-only mean describes whom directly?
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
Among 916 respondents, the mean recorded rating was 4.1 on the stated scale; 284 invitees had no rating, so this does not establish the mean for all 1,200 invitees.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
The same summaries can hide different tails, peaks, gaps or groups. A plot helps reveal structure that matters for the decision.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?