Question

select the correct answer. which data set has the greatest spread for the middle 50% of its data? a. {18, 13, 22, 17, 21, 24} b. {17, 19, 22, 26, 17, 14} c. {13, 17, 12, 21, 18, 20} d. {18, 21, 16, 22, 24, 18}

Explanation:

Step1: Find IQR for each set

The middle 50% spread is the Interquartile Range (IQR) = $Q_3 - Q_1$.

For Set A {18,13,22,17,21,24}:

Sort: {13,17,18,21,22,24}
$Q_1 = \frac{17+18}{2}=17.5$, $Q_3 = \frac{22+24}{2}=23$
IQR = $23 - 17.5 = 5.5$

For Set B {17,19,22,26,17,14}:

Sort: {14,17,17,19,22,26}
$Q_1 = \frac{17+17}{2}=17$, $Q_3 = \frac{19+22}{2}=20.5$
IQR = $20.5 - 17 = 3.5$

For Set C {13,17,12,21,18,20}:

Sort: {12,13,17,18,20,21}
$Q_1 = \frac{13+17}{2}=15$, $Q_3 = \frac{18+20}{2}=19$
IQR = $19 - 15 = 4$

For Set D {18,21,16,22,24,15}:

Sort: {15,16,18,21,22,24}
$Q_1 = \frac{16+18}{2}=17$, $Q_3 = \frac{21+22}{2}=21.5$
IQR = $21.5 - 17 = 4.5$

Step2: Compare all IQR values

IQR values: A=5.5, B=3.5, C=4, D=4.5. The largest is 5.5.

Answer:

A. {18, 13, 22, 17, 21, 24}