Counts, rates and denominators
A count says how many successes happened. A rate says what share of eligible cases succeeded. The denominator chooses the question.
Six passes among ten students is 60%; eight among twenty is 40%. A larger pass count does not imply a higher pass rate. The formula needs eligible units in its denominator.
Suppose A passes three registrations and B fails one. Registration pass rate is 3/4=75%. The proportion of students passing at least one course is 1/2=50%. Both are valid answers to explicitly different questions. A claim about students requires a student-level outcome definition, such as at least one pass, all courses passed or mean course score.
A mean of group means is not necessarily the overall mean. Use valid group sizes as weights if reconstructing a pooled observed numerical mean. For rates, sum successes and eligible denominators, or equivalently weight subgroup rates by their shares of the relevant denominator.
Source: W5 PDF pp. 3-51, 53. The lecture uses both a constructed 200-student support example and a synthetic 4,665-registration course dataset. They are different tables with different units.
The mean of complete 0/1 outcomes is a rate. The denominator is course registrations, linking directly to the later lecture on counts and rates.
An IQR flag describes unusualness, while the dictionary and source establish different evidence. Deleting verified older students changes the population behind a rate.
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.
Six passes out of ten versus eight out of twenty: which has the higher rate?
A passes three courses; B fails one. What share of students passed at least one?
2. Application
Apply the concept to a case or calculation.
Eight successes among twenty eligible cases is what rate?
Group A has 9/10 successes and B has 10/20. What is the pooled rate?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
To report the proportion of students who passed all their courses, what is needed first?
What weights reconstruct a pooled observed numeric mean from group means?
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
One student could pass three courses while another fails one. Three of four registrations passed, but only one of the two students passed any course.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
Multiply each observed mean by its valid count, add those totals, then divide by the total valid count. The weights come from the observations being pooled.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?