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CHAPTER 2
Describing, Exploring, and Comparing Data
the relative frequencies for the three groups. By comparing those relative frequencies, it should be obvious that the frequency distribution for smokers is
very different from the frequency distributions for the other two groups. Because the two groups of nonsmokers (exposed and not exposed) have such
high frequency amounts for the first class, it might be helpful to further compare those data sets with a closer examination of those values.
2-2 Basic Skills and Concepts
In Exercises 1–4, identify the class width, class midpoints, and class boundaries for the
given frequency distribution based on Data Set 1 in Appendix B.
1. Systolic Blood
Frequency
Pressure of Women
Frequency
90–99
100–109
110–119
120–129
130–139
140–149
150–159
1
4
17
12
5
0
1
80–99
100–119
120–139
140–159
160–179
180–199
9
24
5
1
0
1
3. Cholesterol of Men
Table for Exercise 13
Outcome
Frequency
1
2
3
4
5
6
27
31
42
40
28
32
Table for Exercise 14
Digit
Frequency
0
1
2
3
4
5
6
7
8
9
18
12
14
9
17
20
21
26
7
16
2. Systolic Blood
Pressure of Men
0–199
200–399
400–599
600–799
800–999
1000–1199
1200–1399
Frequency
13
11
5
8
2
0
1
4. Body Mass
Index of Women
Frequency
15.0–20.9
21.0–26.9
27.0–32.9
33.0–38.9
39.0–44.9
10
15
11
2
2
In Exercises 5–8, construct the relative frequency distribution that corresponds to the
frequency distribution in the exercise indicated.
5. Exercise 1
6. Exercise 2
7. Exercise 3
8. Exercise 4
In Exercises 9–12, construct the cumulative frequency distribution that corresponds to the
frequency distribution in the exercise indicated.
9. Exercise 1
10. Exercise 2
11. Exercise 3
12. Exercise 4
13. Loaded Die The author drilled a hole in a die and filled it with a lead weight, then
proceeded to roll it 200 times. (Yes, the author has too much free time.) The results
are given in the frequency distribution in the margin. Construct the corresponding relative frequency distribution and determine whether the die is significantly different
from a fair die that has not been “loaded.”
14. Lottery The frequency distribution in the margin is based on the Win Four numbers
from the New York State Lottery, as listed in Data Set 26 in Appendix B. Construct
the corresponding relative frequency distribution and determine whether the results
appear to be selected in such a way that all of the digits are equally likely.
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2-2
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Frequency Distributions
15. Bears Refer to Data Set 9 in Appendix B and construct a frequency distribution of the
weights of bears. Use 11 classes beginning with a lower class limit of 0 and use a
class width of 50 lb.
16. Body Temperatures Refer to Data Set 4 in Appendix B and construct a frequency distribution of the body temperatures for midnight on the second day. Use 8 classes beginning with a lower class limit of 96.5 and use a class width of 0.4°F. Describe two
different notable features of the result.
17. Head Circumferences Refer to Data Set 3 in Appendix B. Construct a frequency distribution for the head circumferences of baby boys and construct a separate frequency
distribution for the head circumferences of baby girls. In both cases, use the classes of
34.0–35.9, 36.0–37.9, and so on. Then compare the results and determine whether
there appears to be a significant difference between the two genders.
18. Animated Movies for Children Refer to Data Set 7 in Appendix B. Construct a frequency distribution for the lengths of time that animated movies for children contain
tobacco use and construct a separate frequency distribution for the lengths of time for
alcohol use. In both cases, use the classes of 0–99, 100–199, and so on. Compare the
results and determine whether there appears to be a significant difference.
19. Marathon Runners Refer to Data Set 8 in Appendix B. Construct a relative frequency
distribution for the ages of the sample of males who finished the New York City
marathon, then construct a separate relative frequency distribution for the ages of the
females. In both cases, start the first class with a lower class limit of 19 and use a
class width of 10. Compare the results and determine whether there appears to be any
notable difference between the two groups.
20. Regular Coke > Diet Coke Refer to Data Set 17 in Appendix B. Construct a relative
frequency distribution for the weights of regular Coke by starting the first class at
0.7900 lb and use a class width of 0.0050 lb. Then construct another relative frequency distribution for the weights of diet Coke by starting the first class at 0.7750 lb
and use a class width of 0.0050 lb. Then compare the results and determine whether
there appears to be a significant difference. If so, provide a possible explanation for
the difference.
2-2 Beyond the Basics
21. Interpreting Effects of Outliers Refer to Data Set 20 in Appendix B for the axial loads
of aluminum cans that are 0.0111 in. thick. The load of 504 lb is called an outlier because it is very far away from all of the other values. Construct a frequency distribution that includes the value of 504 lb, then construct another frequency distribution
with the value of 504 lb excluded. In both cases, start the first class at 200 lb and use
a class width of 20 lb. Interpret the results by stating a generalization about how much
of an effect an outlier might have on a frequency distribution.
Table for Exercise 22
Number
of Values
16–22
23–45
22. Number of Classes In constructing a frequency distribution, Sturges’ guideline suggests that the ideal number of classes can be approximated by 1 1 (log n) > (log 2),
where n is the number of data values. Use this guideline to complete the table for determining the ideal number of classes.
Copyright © 2005 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Ideal Number
of Classes
5
6
7
8
9
10
11
12