What is demonstrated: you correctly distinguish mean as an arithmetic average and median as position-based “middle,” and you notice that 100 can pull the mean. Partial: the rule for even counts is missing. Misconception: “median is better whenever” and “mean becomes wrong” overstate the source; sensitivity does not make a correctly calculated mean wrong, and the choice depends on purpose/data quality. Method error: for four ordered values, 4 is not the median; the two middle values must be combined. Not attempted: checking whether 100 is a genuine value or error, and explaining what “typical” should mean here.
One-shot teach-back worksheet—answer before opening the rubric: Q1 only: For 2, 3, 4, 100, which two observations determine the median, and what single operation combines them? Q2: Explain why the mean can remain mathematically correct but be less useful as a typical value. Q3: Give one reason to check 100 before choosing a summary. Q4: If 100 is verified as a real high value, choose a measure for a “typical observation” and state one limitation of that choice.
Rubric: Q1 identifies 3 and 4 and averages them to 3.5. Q2 distinguishes calculation correctness from representativeness. Q3 treats data error as possible, not certain. Q4 may choose median with skew/extreme justification, while acknowledging it hides magnitude or does not explain cause; another choice is acceptable if purpose is explicit.
Parallel retest: values 5, 6, 7, 8, 54. Success requires correct mean and median method, a purpose-based choice, and one data-quality check—without “always.” Remaining gap after the original response: even-count procedure and conditional choice. Next review: redo one even-count and one verified-extreme scenario tomorrow.
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