Answer
$(6,8, 19, 32, 54)$
$IQR=24$
Work Step by Step
Start finding the five-number summary and IQR by ordering the data:
$6, 8, 12, 19, 27, 32, 54$
Minimum $= 6$
$Q_1$ (first quartile) = median of lower half $= (6, 8, 12) → Q_1 = 8$
Median ($Q_2$) = middle value$ = 19$
$Q_3$ (third quartile) = median of upper half $= (27, 32, 54) → Q_3 = 32$
Maximum $= 54$
So, the five-number summary $= (6, 8, 19, 32, 54)$
Calculate the IQR:
$IQR=Q_3-Q_1=32-8=24.$
