Compute and interpret mean, median, range, and interquartile range in context.
Find every matching center-and-spread representation
Problem
The target is a data set with median \(12\) and range \(8\). Evaluate candidates A–E, then report the \(\text{complete}~\text{matching}~\text{set}\).
A. \(8,~10,~12,~12,~16\) B. \(9,~10,~12,~14,~17\) C. \(12,~12,~12,~16,~20\) D. \(7,~11,~12,~13,~15\) E. \(10,~12,~12,~14,~18\)
Big Picture
What this problem is really about
Apply two independent tests to every ordered five-value set. The third entry must match the target median, and the last entry minus the first must match the target range; satisfying only one condition is insufficient. Repeated middle values are allowed, so judge positions and endpoint differences rather than how varied a list appears.
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