Question

Draw and display a histogram for each of the two variables using appropriate BIN values from part (b) and comment on the shape of the two distributions.

Hours Per Week	Yearly Income ('000's)
18	43.8
13	44.5
18	44.8
25.5	46.0
11.3	41.1
18	43.3
16	43.6
27	46.2
27.5	46.8
30.5	48.2
24.5	49.3
32.5	53.8
25	53.9
23.5	54.2
30.5	50.5
27.5	51.2
28	51.5
26	52.6
25.5	52.8
26.5	52.9
33	49.5
15	49.8
27.5	50.3
36	54.3
27	55.1
34.5	55.3
39	61.7
37	62.3
31.5	63.4
37	63.7
24.5	55.5
28	55.6
19	55.7
38.5	58.2
37.5	58.3
18.5	58.4
32	59.2
35	59.3
36	59.4
39	60.5
24.5	56.7
26	57.8
38	63.8
44.4	64.2
34.5	55.8
34.5	56.2
40	64.3
41.5	64.5
34.5	64.7
42.3	66.1
34.5	72.3
28	73.2
38	74.2
31.5	68.5
36	69.7
37.5	71.2
22	66.3
33.5	66.5
37	66.7
43.5	74.7
20	62.0
35	57.3
24	55.3
24.3	55.6

The researcher suggests using class intervals as 10 < X ≤ 15, 15 < X ≤ 20, …, 40 < X ≤ 45 for the hours per week variable and class intervals 40 < X ≤ 45, 45 < X ≤ 50, ..., 70 < X ≤ 75 for the yearly income variable.

Answer 1

1) Hours per week       Using the given bins, we create the class table

Using Excel function Histogram in Data->Data Analysis, we plot the histogram as below

Fill the frequency obtained in the table above

Comment on the distribution     
The distribution appears to be left skewed as its long tail is on the left side      

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2) Yearly Income ('000s)                       Using the given bins, we create the class table

Using Excel function Histogram in Data->Data Analysis, we plot the histogram as below

Fill the frequency obtained in the table above

Comment on the distribution              
The distribution appears to be approximately normal as the shape is symmetric bell shaped              

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