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M1-052-A09-V02
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S-ID.3
Warmup
M1-052-A09-V02
Interpret differences in shape, center, spread, and outliers in context.
Choose a contextual conclusion supported by display evidence
Problem
Interpret this histogram evidence and its limits: \(\text{two}~\text{commute}~\text{distributions}\) have similar center bins, but B has a longer right tail. State the center and tail meanings, a supported contextual conclusion, and claims the display does not support.
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A
center evidence=similar center bins→B usually longer; tail evidence=B extends farther toward high times→more long commutes; supported=B has longer typical commutes; unsupported=tail alone cannot determine B's exact median
B
center evidence=similar center bins→similar typical commute region; tail evidence=B extends farther toward high times→more long commutes/high-end variability; supported=typical commutes appear similar but B has more long commutes; unsupported=B's exact median or every B commute is larger
C
center evidence=similar center bins→identical commute times; tail evidence=B has longer right tail→same variability; supported=identical distributions; unsupported=any difference can be inferred
D
center evidence=similar center bins→similar typical commute region; tail evidence=B extends farther toward high times→A has more long commutes; supported=A has more long commutes; unsupported=tail direction is relevant
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Curriculum context
Standard S-ID.3
Category Statistics and Probability
Domain Interpreting Categorical and Quantitative Data
Objective Interpret differences in shape, center, spread, and outliers in context.
Problem type Choose a contextual conclusion supported by display evidence