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WEEK 3 · INDEPENDENT PRACTICE

Distribution, centre and variation

Concepts, calculations, scientific claims and a formative self-check.

4 × 5 = 20 marks30–45 minutesNo R required

Scenario: Consider five fictional values: 4, 5, 6, 7 and 38. How does an extreme observation affect summaries?

Use the fictional dataset if the question refers to it. Always show your reasoning; an exact number without context is not enough. The four written tasks are teacher-assessed. The self-check below is formative and does not affect the 20-mark assignment.

Written problem set

TASK 1 · 5 MARKS

Define and frame

Calculate mean and median for 4, 5, 6, 7 and 38. Which might better represent a typical case, and why?

TASK 2 · 5 MARKS

Calculate or apply

Give R commands for the mean and median of score_post and a check for missing values.

TASK 3 · 5 MARKS

Evaluate the design

One group has a higher mean but much wider scores. Why is mean-only comparison risky?

TASK 4 · 5 MARKS

Interpret and communicate

Say when to choose a histogram rather than a boxplot. Specify appropriate axis labels.

Standard scoring guide

Each written task is worth 5 points: correct key idea (2), justified application or computation (2), and a clear statement with limits (1). This original rubric is not official UCL assessment.

Formative self-check · 4 questions

Choose one answer for each item, then check the feedback. Answers and explanations are available on this public study page; the separate written-task instructor key is private.

1. What is the median of 4,5,6,7,38?
2. What is the mean of those five values?
3. Which display helps compare numerical distributions by group?
4. What does standard deviation primarily describe?