The researcher wishes to use graphical descriptive methods to present summaries of the data on each of the two variables: hours worked per week and yearly income Hours Per Week Yearly Income ('000's) 18 43.8 13 44.5 18 44.8 25.5 46.0 11.5 41.2 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 44.5 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 74.8 20 62.0 35 57.3 24 55.3 20 56.1 41 61.5 a) The number of observations (n) is 65 individuals. The researcher suggests using 7 class intervals to construct a histogram for each variable. Expain hoe the reseacher would have decided on the numbet of class intervals (K) as 7 b) 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. Explain how the researcher would have decided the width of the above class intervals (or class width). c) 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.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.6: Rational Functions

Problem 11SC: Find the mean hourly cost when the cell phone described above is used for 240 minutes.

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The researcher wishes to use graphical descriptive methods to present summaries of the data on each of the two variables: hours worked per week and yearly income

Hours Per Week	Yearly Income ('000's)
18	43.8
13	44.5
18	44.8
25.5	46.0
11.5	41.2
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
44.5	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	74.8
20	62.0
35	57.3
24	55.3
20	56.1
41	61.5

a) The number of observations (n) is 65 individuals. The researcher suggests using 7 class intervals to construct a histogram for each variable. Expain hoe the reseacher would have decided on the numbet of class intervals (K) as 7
b) 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. Explain how the researcher would have decided the width of the above class
intervals (or class width).
c) 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.

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