Q 63. - The Practice of Statistics for AP

Question

Who makes more? A manufacturing company is reviewing the salaries of its full-time employees below the executive level at a large plant. The clerical staff is almost entirely female, while a majority of the production workers and technical staff are male. As a result, the distributions of salaries for male and female employees may be quite different. The table below gives the frequencies and relative frequencies for women and men. 

(a) Explain why the total for women is greater than $100\%$

(b) Make histograms for these data, choosing the vertical scale that is most appropriate for comparing the two distributions.

(c) Write a few sentences comparing the salary distributions for men and women.

Step-by-Step Solution

Answer

Part (a) This deviation of $0.1\%$

Part (c) Shape: right-skewed

Center: higher for men than for women

Spread: men are more than the women

Part (b) 

Part (a) Step 1: Given information

Salary	Number	%	Number	%
10-15	89	11.8	26	1.1
15-20	192	25.4	221	9.0
20.25	236	31.2	677	27.6
25-30	111	14.7	823	33.6
30-35	86	11.4	365	14.9
35-40	25	3.3	182	7.4
40-45	11	1.5	91	3.7
50-55	2	0.3	19	0.8
55-60	0	0.0	11	0.4
60-65	0	0.0	0	0.0
65-70	1	0.1	3	0.1
Total	756	100.1	2451	100.0

Part (a) Step 2: Concept

A histogram is a graphing tool that is extensively used. It's used to summarise discrete or continuous data measured on a scale of one to ten. It's a standard way of exhibiting essential data distribution aspects in an easy-to-understand format. 

Part (a) Step 3: Explanation

We should point out that the number for women is $100.1$ percent rather than $100$ percent.

This $0.1$ percent difference is most likely due to rounding error.

Part (b) Step 1: Explanation

The first bar has a width of $5$ and runs from $10$ to $15$ The other bars are nearby and have a width of $10$ The bar must be the same height as the percent.

Thus, the histogram is made.

Part (c) Step 1: Explanation

Shape: Because the tallest bars are on the left of the histogram, both distributions are right-skewed.

Center: Because men's tallest bar is more to the right than women's, the center is higher for males than for women.

Spread: The spread for males is greater than the spread for women because men's histograms have one more bar (not nearly zero) than women's histograms.