Question

28 the ages of the last 16 united states presidents on their first inauguration day are shown in the table below. determine the interquartile range for this set of data.
51 54 51 60
62 43 55 56
61 52 69 64
46 54 47 70

Explanation:

Step1: Arrange data in ascending order

$43,46,47,51,51,52,54,54,55,56,60,61,62,64,69,70$

Step2: Find the median (Q2)

Since $n = 16$ (even), $Q2=\frac{54 + 55}{2}=54.5$

Step3: Find the lower half of data

$43,46,47,51,51,52,54,54$. The median of this lower - half (Q1) is $\frac{51+51}{2}=51$

Step4: Find the upper half of data

$55,56,60,61,62,64,69,70$. The median of this upper - half (Q3) is $\frac{61 + 62}{2}=61.5$

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=61.5−51 = 10.5$

Answer:

$10.5$