Part 1
Assignment Submission & Scoring
Assignment Submission
For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.
Assignment Scoring
Your last submission is used for your score.
1.
[â€“/1 Points]
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What is the difference between a class boundary and a class limit? (Select all that apply.)
Class boundaries are values halfway between the upper class limit of one class and the lower class limit of the next.
Class limits are possible data values.
Class boundaries are possible data values.
Class boundaries are not possible data values.
Class limits are not possible data values.
Class boundaries specify the span of data values that fall within a class.
Class limits specify the span of data values that fall within a class.
Class limits are values halfway between the upper class boundary of one class and the lower class boundary of the next.
2.
[â€“/15 Points]
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A data set with whole numbers has a low value of 20 and a high value of 96.
Find the class width for a frequency table with seven classes.
Find the class limits for a frequency table with seven classes.
3.
[â€“/19 Points]
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Look at the histogram below, which shows mileage, in kilometers per liter (km/L), for a random selection of diverse makes and aged passenger cars.â€
(a) Is the shape of the histogram essentially bimodal?
Yes, because the histogram has one peak.
Yes, because the histogram has two peaks.Â Â Â Â
No, because the histogram has one peak.
No, because the histogram has two peaks.
(b) Jose looked at the raw data and discovered that the 54 data values included both the city and highway mileages for 27 cars. He used the city mileages for the 27 cars to make the histogram below.
Using this information and the histograms shown above, construct a frequency table for the highway mileages of the same cars. Use class boundaries 16.5, 20.5, 24.5, 28.5, 32.5, 36.5, and 40.5.
Class Boundaries
Frequency
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
4.
[â€“/4 Points]
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The following data represent salaries, in thousands of dollars, for employees of a small company. Notice the data have been sorted in increasing order.
54
55
55
57
57
59
60
65
65
65
66
68
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70
70
70
75
75
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75
77
82
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82
88
89
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91
91
97
98
98
98
280
(a) Make a histogram using the class boundaries 53.5, 99.5, 145.5, 191.5, 237.5, 283.5.
(b) Look at the last data value. Does it appear to be an outlier? Could this be the owner's salary?
Yes, it is an outlier and it is likely the owner's salary.
Yes, it is an outlier, but it is not likely the owner's salary.Â Â Â Â
No, it is not an outlier, but it is likely the owner's salary.
No, it is not an outlier and it is not likely the owner's salary.
(c) Eliminate the high salary of 280 thousand dollars. Make a new histogram using the class boundaries 53.5, 62.5, 71.5, 80.5, 89.5, 98.5.
Does this histogram reflect the salary distribution of most of the employees better than the histogram in part (a)?
Yes
NoÂ Â Â Â
5.
[â€“/20 Points]
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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on the next page are based on random samples of size 30, 50, and 100 from the same population.
26
27
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30
25
26
27
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30
26
27
28
29
30
x
x
x
(a) Using the midpoint labels of the three histograms, what would you say about the estimated range of the population data from smallest to largest? Does the bulk of the data seem to be between 26 and 30 in all three histograms?
(b) The population distribution from which the samples were drawn is symmetric and moundshaped, with the top of the mound at 10, 95% of the data between 26 and 30, and 99.7% of data between 25 and 31. How well does each histogram reflect these characteristics?
6.
[â€“/4 Points]
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The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars.
(i) Ogive
(ii) Ogive Showing Cumulative Percentage of Data
(a) How were the percentages shown in graph (ii) computed?
The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph (i) by 100 and then converting those values into decimals.
The percentages in graph (ii) were computed by multiplying each of the cumulative frequencies in graph (i) by 50 and then converting those values into percents.Â Â Â Â
The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph (i) by 50 and then converting those values into fractions.
The percentages in graph (ii) were computed by multiplying each of the cumulative frequencies in graph (i) by 100 and then converting those values into decimals.
The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph (i) by 50 and then converting those values into percents.
(b) How many states have average per capita income less than 37.5 thousand dollars?
(c) How many states have average per capita income between 42.5 and 52.5 thousand dollars?
(d) What percentage of the states have average per capita income more than 47.5 thousand dollars?
%
7.
[â€“/6 Points]
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The following ogives come from different distributions of 50 whole numbers between 1 and 60. Labels on each point give the cumulative frequency and the cumulative percentage of data.
(a) In which distribution does the most data fall below 20.5?
(b) In which distribution does the most data fall below 40.5?
(c) In which distribution does the amount of data below 20.5 most closely match that above 30.5?
(d) Which distribution seems to be skewed right?
Which distribution seems to be skewed left?
Which distribution seems to be moundshaped?
8.
[â€“/45 Points]
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How long does it take to finish the 1868 km Iditarod Dog Sled Race from Anchorage to Nome, Alaska? Finish times (to the nearest hour) for 57 dogsled teams are shown below.
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333
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283
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307
328
285
291
295
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315
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318
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333
321
323
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327
For this problem, use five classes.
(a) Find the class width.
(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 2 decimal places.)
Class Limits
Class Boundaries
Midpoint
Frequency
Relative
Frequency
Cumulative
Frequency
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
(c) Draw a histogram.
(d) Draw a relativefrequency histogram.
(e) Categorize the basic distribution shape.
uniform
imodalÂ Â Â Â
skewed right
moundshaped symmetrical
skewed left
(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)
Selection Tool
Line
Ray
Segment
Circle
Vertical Parabola
Horizontal Parabola
Point
No Solution
Help
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Clear Graph
Delete Laye
Fill
WebAssign Graphing Tool
Graph Layers
Toggle Open/Closed
Â· After you add an object to the graph you can use Graph Layers to view and edit its properties.
9.
[â€“/45 Points]
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What percent of undergraduate enrollment in coed colleges and universities in the United States is male? A random sample of 50 such institutions give the following data.
Percent Males Enrolled in Coed Universities and Colleges
55
46
48
26
37
48
37
45
44
40
46
27
44
49
37
56
37
68
57
26
45
43
43
56
55
46
53
42
52
54
43
39
77
48
49
39
62
46
41
46
57
37
39
40
58
55
50
27
57
42
For this problem, use five classes.
(a) Find the class width.
(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to two decimal places.)
Class Limits
Class Boundaries
Midpoint
Frequency
Relative
Frequency
Cumulative
Frequency










(c) Draw a histogram.
(d) Draw a relativefrequency histogram.
(e) Categorize the basic distribution shape.
moundshaped symmetric
uniform or rectangularÂ Â Â Â
skewed left
skewed right
imodal
(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.Â This cannot be done in SALT.)
Selection Tool
Line
Ray
Segment
Circle
Vertical Parabola
Horizontal Parabola
Point
No Solution
Help
0,0
10
20
30
40
50
60
70
80
90
5
10
15
20
25
30
35
40
45
50
55
60
Clear Graph
Delete Laye
Fill
WebAssign Graphing Tool
Graph Layers
Toggle Open/Closed
Â· After you add an object to the graph you can use Graph Layers to view and edit its properties.
10.
[â€“/53 Points]
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"Readability Levels of Magazine Ads," by F.K. Shuptrine and D.D. McVicker, is an article in the Journal of Advertising Research. The following is a list of the number of threesyllable (or longer) words in advertising copy of randomly selected magazine advertisements.
34Â Â Â Â
21Â Â Â Â
37Â Â Â Â
31Â Â Â Â
10Â Â Â Â
24Â Â Â Â
39Â Â Â Â
10Â Â Â Â
17Â Â Â Â
18Â Â Â Â
32Â Â Â Â
17Â Â Â Â
3Â Â Â Â
10Â Â Â Â
6Â Â Â Â
5Â Â Â Â
6Â Â Â Â
6Â Â Â Â
13Â Â Â Â
22Â Â Â Â
25Â Â Â Â
3Â Â Â Â
5Â Â Â Â
2Â Â Â Â
9Â Â Â Â
3Â Â Â Â
0Â Â Â Â
4Â Â Â Â
29Â Â Â Â
26Â Â Â Â
5Â Â Â Â
5Â Â Â Â
24Â Â Â Â
15Â Â Â Â
3Â Â Â Â
8Â Â Â Â
16Â Â Â Â
9Â Â Â Â
10Â Â Â Â
3Â Â Â Â
12Â Â Â Â
10Â Â Â Â
10Â Â Â Â
10Â Â Â Â
11Â Â Â Â
12Â Â Â Â
13Â Â Â Â
1Â Â Â Â
9Â Â Â Â
43Â Â Â Â
13Â Â Â Â
14Â Â Â Â
32Â Â Â Â
24Â Â Â Â
15Â Â Â Â
Use eight classes.
(a) Find the class width.
(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to two decimal places.)
Class Limits
Class Boundaries
Lower âˆ’ Uppe
Lower âˆ’ Uppe
Midpoint
Frequency
Relative
Frequency
Cumulative
Frequency
0 âˆ’ 5
âˆ’
6 âˆ’ 11
âˆ’
12 âˆ’ 17
âˆ’
18 âˆ’ 23
âˆ’
24 âˆ’ 29
âˆ’
30 âˆ’ 35
âˆ’
36 âˆ’ 41
âˆ’
42 âˆ’ 47
âˆ’
(c) Draw a histogram.
(d) Draw a relativefrequency histogram.
(e) Categorize the basic distribution shape.
moundshaped symmetrical
skewed rightÂ Â Â Â
imodal
skewed left
uniform
(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.Â This cannot be done in SALT.)
Selection Tool
Line
Ray
Segment
Circle
Vertical Parabola
Horizontal Parabola
Point
No Solution
Help
0,0
6
12
18
24
30
36
42
48
5
10
15
20
25
30
35
40
45
50
55
60
Clear Graph
Delete Laye
Fill
WebAssign Graphing Tool
Class Boundaries
Frequency
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
54
55
55
57
57
59
60
65
65
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68
68
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70
70
70
75
75
75
75
77
82
82
82
88
89
89
91
91
97
98
98
98
280
(i) Ogive
(ii) Ogive Showing Cumulative Percentage of Data
261
271
236
244
279
296
284
299
288
288
247
256
338
360
341
333
261
266
287
296
313
311
307
307
299
303
277
283
304
305
288
290
288
289
297
299
332
330
309
328
307
328
285
291
295
298
306
315
310
318
318
320
333
321
323
324
327
Class Limits
Class Boundaries
Midpoint
Frequency
Relative
Frequency
Cumulative
Frequency
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
âˆ’
Percent Males Enrolled in Coed Universities and Colleges
55
46
48
26
37
48
37
45
44
40
46
27
44
49
37
56
37
68
57
26
45
43
43
56
55
46
53
42
52
54
43
39
77
48
49
39
62
46
41
46
57
37
39
40
58
55
50