Question

question 3 of 6
how many pairs of shoes does a typical teenage boy own? to find out, a group of statistics students surveyed 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 dotplot.
14 7 6 5 12 38 8 7 10 10 10 11 4 5 22 7 5 10 35 7
find the interquartile range of the distribution.
iqr = 45 pairs of shoes (enter an integer)

Explanation:

Step1: Sort the data

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

Step2: Find the median (Q2)

Since there are \(n = 20\) data - points, the median is the average of the 10th and 11th ordered values. The 10th value is 7 and the 11th value is 7, so \(Q2=\frac{7 + 7}{2}=7\).

Step3: Find the lower half and Q1

The lower half of the data consists of the first 10 values: 4, 5, 5, 5, 5, 6, 7, 7, 7, 7. Since \(n = 10\) (even), \(Q1=\frac{5+6}{2}=5.5\).

Step4: Find the upper half and Q3

The upper half of the data consists of the last 10 values: 8, 10, 10, 10, 10, 10, 11, 12, 14, 22, 35, 38. Since \(n = 10\) (even), \(Q3=\frac{10 + 10}{2}=10\).

Step5: Calculate the IQR

\(IQR=Q3 - Q1=10 - 5.5 = 4.5\)

Answer:

4.5