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: Find the median (Q2)

The data set has 12 values. The median is the average of the 6th and 7th values. The 6th value is 21, the 7th is 21. So median \( Q2=\frac{21 + 21}{2}=21 \).

Step2: Find Q1 (median of lower half)

Lower half: 8, 11, 14, 16, 17, 21. There are 6 values, median is average of 3rd and 4th. 3rd:14, 4th:16. So \( Q1=\frac{14 + 16}{2}=15 \).

Step3: Find Q3 (median of upper half)

Upper half:21, 24, 27, 31, 43, 47. Median is average of 3rd and 4th. 3rd:27, 4th:31. So \( Q3=\frac{27 + 31}{2}=29 \).

Step4: Calculate IQR

IQR = Q3 - Q1 = \( 29 - 15 = 14 \).

IQR tells the spread of the data around the median. It represents the middle 50% (since IQR is between Q1 and Q3, which covers 50% of data) of the heights.

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.