Download 3. Unusual Value? A statistics professor gives a test that has a mean

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3-3
Measures of Variation
3. Unusual Value? A statistics professor gives a test that has a mean of 50 and a standard deviation of 10. (She is not using a typical test with a maximum score of 100,
and she promises to curve the scores.) One student earns a score of 85 on this test. In
this context, is the score of 85 “unusual”? Why or why not?
4. Correct Statement? In the book How to Lie with Charts, Gerald E. Jones writes that
“the standard deviation is usually shown as plus or minus the difference between the
high and the mean, and the low and the mean. For example, if the mean is 1, the high
3, and the low 21, the standard deviation is 62.” Is that statement correct? Why or
why not?
In Exercises 5–12, find the range, variance, and standard deviation for the given sample
data. (The same data were used in Section 3-2 where we found measures of center. Here
we find measures of variation.) Also, answer the given questions.
5. Perception of Time Statistics students participated in an experiment to tests their ability to determine when 1 minute (or 60 seconds) has passed. The results are given below in seconds. Identify at least one good reason why the standard deviation from this
sample might not be a good estimate of the standard deviation for the population of
adults.
53
52
75
62
68
58
49
49
6. Cereal A dietician obtains the amounts of sugar (in centigrams) from 100 centigrams
(or 1 gram) in each of 10 different cereals, including Cheerios, Corn Flakes, Fruit
Loops, and 7 others. Those values are listed below. Is the standard deviation of those
values likely to be a good estimate of the standard deviation of the amounts of sugar
in each gram of cereal consumed by the population of all Americans who eat cereal?
Why or why not?
3
24
30
47
43
7
47
13
44
39
7. Phenotypes of Peas An experiment was conducted to determine whether a deficiency
of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype codes, where 1 smooth-yellow, 2 smooth-green, 3 wrinkled-yellow,
and 4 wrinkled-green. Can the measures of variation be obtained for these values?
Do the results make sense?
2 1 1 1 1 1 1 4 1 2 2 1 2 3 3 2 3 1 3 1 3 1 3 2 2
8. Old Faithful Geyser Listed below are intervals (in minutes) between eruptions of the
Old Faithful geyser in Yellowstone National Park. Based on the results, is an interval
of 100 minutes unusual?
98
92
95
87
96
90
65
92
95
93
98
94
9. Blood Pressure Measurements Fourteen different second-year medical students at
Bellevue Hospital measured the blood pressure of the same person. The systolic readings (in mmHg) are listed below. If the subject’s blood pressure remains constant and
the medical students correctly apply the same measurement technique, what should
be the value of the standard deviation?
138 130 135 140 120 125 120 130 130 144 143 140 130 150
10. Body Temperatures Researchers at the University of Maryland collected body temperature readings from a sample of adults, and eight of those temperatures are listed
below (in degrees Fahrenheit). Based on these results, is a body temperature of
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