Question

the heights, in feet, of 12 trees in a park are shown below. 8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47. use the drop - down menus to explain the interquartile range of the data. click the arrows to choose an answer from each menu. the interquartile range helps tell the choose... of the data around the choose... . the interquartile range, which is choose... feet, represents choose... of the heights of the trees.

Explanation:

Step1: Arrange data in ascending order

$8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47$

Step2: Find the median (Q2)

Since $n = 12$ (even), $Q2=\frac{21 + 21}{2}=21$

Step3: Find the lower half data

$8, 11, 14, 16, 17, 21$. Median of lower - half (Q1) is $\frac{14+16}{2}=15$

Step4: Find the upper half data

$21, 24, 27, 31, 43, 47$. Median of upper - half (Q3) is $\frac{27 + 31}{2}=29$

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1=29 - 15 = 14$

The interquartile range helps tell the spread of the data around the median. The interquartile range, which is 14 feet, represents the middle 50% of the heights of the trees.

Answer:

The interquartile range helps tell the spread of the data around the median. The interquartile range, which is 14 feet, represents the middle 50% of the heights of the trees.