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 the range for women

In a box - plot, the range is the difference between the maximum and minimum values. For women, the minimum value is around 2 and the maximum value is around 24. So the range for women $R_w=24 - 2=22$.

Step2: Find the range for men

For men, the minimum value is around 0 and the maximum value is around 16. So the range for men $R_m=16 - 0 = 16$.

Step3: Calculate the difference in ranges

The difference in ranges $\Delta R=R_w - R_m=22-16 = 6$.

Step4: Identify the median for women and men

In a box - plot, the line inside the box represents the median. For women, the median is around 14. For men, the median is around 6. So women have the highest median.

Step5: Estimate the number of women with 10 - 18 pairs of shoes

The box in a box - plot represents the inter - quartile range (IQR), which contains about 50% of the data. The box for women starts at around 10 and ends at around 18. Since there are 40 women surveyed, the number of women with 10 - 18 pairs of shoes is about $0.5\times40 = 20$.

Answer:

1. 6
2. Women
3. 20