Worked eight-number calculation
Writing the steps makes your answer easier to check and helps you avoid mixing sample and population formulas.
Additional practice example, not your personalised Lab 2 output: 35, 40, 45, 50, 60, 65, 70, 75 points.
| Quantity | Calculation and answer |
|---|---|
| Sum and n | 440 points; n = 8 |
| Mean | 440 / 8 = 55 points |
| Median | (50 + 60) / 2 = 55 points |
| Deviations | -20, -15, -10, -5, 5, 10, 15, 20 |
| Squared deviations | 400, 225, 100, 25, 25, 100, 225, 400 |
| Sum of squared deviations | 1,500 points squared |
| Sample variance and SD | 1,500 / 7 = 214.286 points squared; SD = 14.639 points |
| Population variance and SD | 1,500 / 8 = 187.5 points squared; SD = 13.693 points |
Show the intermediate steps in a hand-calculation question. Round the final answer, not each intermediate deviation or fitted parameter.
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 mean and SD formulas in the lecture are applied to your eight generated scores. The code checks your working after you try it.
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.
The eight practice scores sum to 440. What is their mean?
For n=8 and squared deviations summing to 1,500, what is sample variance?
2. Application
Apply the concept to a case or calculation.
For eight sorted values, which positions determine the numeric median?
What should the deviations from the sample mean sum to, apart from rounding?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Squared deviations total 1,500 for eight scores. What is population-style variance?
Which is a correct sample-SD report for the eight-score example?
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
There are eight sorted values. The median is the average of positions 4 and 5: (50+60)/2=55. A summary need not be an observed value.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
It divides the same squared-deviation total by 8, giving 187.5 points squared, rather than dividing by 7 for sample variance.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?