Question

practice problem: 24. students from a statistics class were asked to record their heights in inches: 65 72 68 64 60 55 73 71 52 63 61 65 74 69 67 74 50 44 75 67 62 66 80 64 construct a modified boxplot of the data.

Explanation:

Step1: Sort the data.

$44,50,52,55,60,61,62,63,64,64,65,65,65,66,67,67,68,69,71,72,73,74,74,75,80$

Step2: Find quartiles.

$Q_1 = 60, Q_2=65, Q_3 = 71$

Step3: Calculate IQR.

$IQR=Q_3 - Q_1=71 - 60 = 11$

Step4: Determine fences.

Lower fence: $Q_1-1.5\times IQR=60 - 1.5\times11 = 43.5$
Upper fence: $Q_3 + 1.5\times IQR=71+1.5\times11 = 87.5$

Step5: Construct box - plot.

Plot minimum (44), $Q_1$, $Q_2$, $Q_3$, maximum (80) and draw box and whiskers.

Answer:

Box - plot constructed as described above.