Question

question 1 of 6
how many pairs of shoes does a typical teenage boy own? to find out, a group of statistics students surveys a random sample of 20 male students from their large high school. then they recorded the number of pairs of shoes that each boy owned. here are the data, along with a dot - plot.
14 7 6 5 12 38 8 7 10 10 10 11 4 5 22 7 5 10 35 7
0 5 10 15 20 25 30 35 40
pairs of shoes
find the interquartile range of the distribution.
iqr = pairs of shoes (enter an integer)
interpret the interquartile range.
the iqr describes how much the number of shoes owned by these teenage boys typically varies from the mean.
the iqr gives the average number of shoes owned by the teenage boys in the sample.
the iqr gives the range of the middle half of number of pairs of shoes for this random sample of 20 male students.

Explanation:

Step1: Sort the data

4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 10, 10, 10, 10, 11, 12, 14, 22, 35, 38

Step2: Find the median (Q2)

Since \(n = 20\) (even), \(Q2=\frac{8 + 10}{2}=9\)

Step3: Find the lower half

4, 5, 5, 5, 6, 7, 7, 7, 7, 8. The median of the lower - half (Q1) is 6.

Step4: Find the upper half

10, 10, 10, 10, 11, 12, 14, 22, 35, 38. The median of the upper - half (Q3) is 12.

Step5: Calculate the IQR

\(IQR=Q3 - Q1=12 - 6 = 6\)

Answer:

6
The IQR gives the range of the middle half of number of pairs of shoes for this random sample of 20 male students.