Two boxplots summarise lists $L_1$ and $L_2$. Median of $L_1 \approx 450$ and median of $L_2 \approx 550$. Range of $L_1 \approx 520$; range of $L_2 \approx 500$. IQR of $L_1 \approx 430$; IQR of $L_2 \approx 220$. Which statement is **best supported**?
A$L_2$ has a higher median **and** greater spread than $L_1$.
B$L_2$ has a higher median, while $L_1$ has greater spread (by both range and IQR).
C$L_1$ has both a higher median and greater spread.
DThe two lists have identical centre and spread.
Answer & Solution
Correct answer: B. $L_2$ has a higher median, while $L_1$ has greater spread (by both range and IQR).
Centre: $L_2$ median ($\sim 550$) > $L_1$ median ($\sim 450$). ✓
Spread: $L_1$ range ($520$) > $L_2$ range ($500$); $L_1$ IQR ($430$) > $L_2$ IQR ($220$). Both spread measures favour $L_1$.
So: $L_2$ higher centre, $L_1$ wider spread.
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