For the data set $\{2, 4, 4, 5, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9\}$, the range is $9 - 2 = 7$, $Q_{1} = 6$, and $Q_{3} = 8.5$. What is the **interquartile range** (IQR)?
A$2.5$
B$3$
C$6$
D$8.5$
Answer & Solution
Correct answer: A. $2.5$
IQR $= Q_{3} - Q_{1} = 8.5 - 6 = 2.5$.
IQR measures the spread of the **middle half** of the data — less sensitive to outliers than the full range.
- Trap C and D restate $Q_1$/$Q_3$ without subtracting.
- Trap B is a guess.
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