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 order

The data 8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47 is already in ascending - order.

Step2: Find the median (Q2)

Since \(n = 12\) (even), \(Q2=\frac{6^{th}\text{ value}+7^{th}\text{ value}}{2}=\frac{21 + 21}{2}=21\).

Step3: Find Q1

The lower half of the data is 8, 11, 14, 16, 17, 21. Since \(n = 6\) (even), \(Q1=\frac{14+16}{2}=15\).

Step4: Find Q3

The upper half of the data is 21, 24, 27, 31, 43, 47. Since \(n = 6\) (even), \(Q3=\frac{27 + 31}{2}=29\).

Step5: Calculate the inter - quartile range (IQR)

\(IQR=Q3 - Q1=29-15 = 14\).
The inter - quartile range helps tell the spread of the data around the median. The inter - quartile range, which is 14 feet, represents the middle 50% of the heights of the trees.

Answer:

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