Question

the box plot shows the results of a survey that asked men and women how many pairs of shoes they own. number of women surveyed - 40 mean of womens data = 14 number of men surveyed - 35 mean of mens data = 8 1. what is the difference between the range of womens pairs of shoes and mens pairs of shoes? 2. who has the highest median pairs of shoes? 3. about how many of the women surveyed would you expect to own between 10 and 18 pairs of shoes?

Explanation:

Step1: Find range of women's shoes

Range is max - min. From box - plot, for women, max = 24, min = 4. So range of women's shoes is \(24 - 4=20\).

Step2: Find range of men's shoes

For men, max = 14, min = 2. So range of men's shoes is \(14 - 2 = 12\).

Step3: Calculate difference in ranges

Difference is \(20-12 = 8\).

Step4: Analyze median for question 2

From box - plot, median of women's data (middle line in box) is higher than median of men's data.

Step5: Analyze for question 3

The box in box - plot represents the inter - quartile range (IQR). For women, the box is from 10 to 18. The IQR contains about 50% of the data. Since 40 women were surveyed, about \(0.5\times40 = 20\) women are expected to own between 10 and 18 pairs of shoes.

Answer:

1. 8
2. Women
3. 20