U.S. Census data for San Luis Obispo County
3.26 ● U.S. Census data for San Luis Obispo County, California, were used to construct the following frequency distribution for commute time (in minutes) of working adults (the given frequencies were read from a graph that appeared in the San Luis Obispo Tribune [September 1, 2002] and so are only approximate):
|
1280
|
5320
|
4390
|
2100
|
1240
|
3060
|
4770
|
1050
|
|
360
|
3330
|
3380
|
340
|
1000
|
960
|
1320
|
530
|
|
3350
|
540
|
3870
|
1250
|
2400
|
960
|
1120
|
2120
|
|
450
|
2250
|
2320
|
2400
|
3150
|
5700
|
5220
|
500
|
|
1850
|
2460
|
5850
|
2700
|
2730
|
1670
|
100
|
5770
|
|
3150
|
1890
|
510
|
240
|
396
|
1419
|
2109
|
|
|
|
Commute
Time Frequency
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0 to 5
|
5,200
|
|
|
5 to 10
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18,200
|
|
10 to 15
|
19,600
|
|
15 to 20
|
15,400
|
|
20 to 25
25 to 30
|
13,800
5,700
|
a. Construct a stem-and-leaf display for these data using the thousands digit as the stem. Comment on the various
|
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30 to 35
|
10,200
|
features of the display.
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35 to 40
|
2,000
|
b. Construct a histogram using class boundaries of 0 to
|
|
40 to 45
|
2,000
|
1000, 1000 to 2000, and so on. How would you describe
|
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45 to 60
|
4,000
|
the shape of the histogram?
|
|
60 to 90
|
2,100
|
c. What proportion of subdivisions has total length less
|
|
90 to 120
|
2,200
|
than 2000? between 2000 and 4000?
|
a. Notice that not all intervals in the frequency distribu- tion are equal in width. Why do you think that unequal width intervals were used?
b. Construct a table that adds a relative frequency and a density column to the given frequency distribution.
c. Use the densities computed in Part (b) to construct a histogram for this data set. (Note: The newspaper dis- played an incorrectly drawn histogram based on frequen- cies rather than densities!) Write a few sentences com- menting on the important features of the histogram.
d. Compute the cumulative relative frequencies, and con- struct a cumulative relative frequency plot.
e. Use the cumulative relative frequency plot constructed in Part (d) to answer the following questions.
i. Approximately what proportion of commute times were less than 50 min?
ii. Approximately what proportion of commute times were greater than 22 min?
iii. What is the approximate commute time value that separates the shortest 50% of commute times from the longest 50%?
Answers
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Posted 09 May 2017 11:05 AM
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