Download Chapter 3 - Practice Problems 1

Chapter 3 - Practice Problems 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) The two most frequently used measures of central tendency are the mean and the median.
Compare these two measures for the following characteristics: Takes every score into
account? Affected by extreme scores? Advantages.
2) Without calculating the standard deviation, compare the standard deviation for the
following three data sets. (Note: All data sets have a mean of 30.) Which do you expect to
have the largest standard deviation and which do you expect to have the smallest
standard deviation? Explain your answers in terms of the formula
∑(x - x)2 .
s =
n-1
1)
2)
30, 30, 30, 30, 30, 30, 30, 30, 30, 30
20, 25, 25, 30, 30, 30, 30, 35, 35, 40
20, 20, 20, 25, 25, 35, 35, 40, 40, 40
3) A company advertises an average of 42,000 miles for one of its new tires. In the
manufacturing process there is some variation around that average. Would the company
want a process that provides a large or a small variance? Justify your answer.
3)
4) Marla scored 85% on her last unit exam in her statistics class. When Marla took the SAT
exam, she scored at the 85 percentile in mathematics. Explain the difference in these two
scores.
4)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the mean for the given sample data.
5) Six college buddies bought each other Christmas gifts. They spent:
5)
$256.51 $264.95 $239.33
$277.03 $129.57 $236.91
What was the mean amount spent? Round your answer to the nearest cent.
A) $351.08
B) $234.05
C) $268.86
D) $280.86
Find the median for the given sample data.
6) The distances traveled (in miles) to 7 different swim meets are given below:
6)
10, 24, 40, 52, 68, 68, 90
Find the median distance traveled.
A) 50 miles
B) 52 miles
C) 40 miles
D) 68 miles
7) The weights (in ounces) of 21 cookies are shown. Find the median weight.
0.73 1.35 0.68 1.62 0.87 0.78 1.32
1.35 1.53 0.92 0.73 1.35 1.09 0.85
0.47 1.35 0.78 1.09 1.72 0.87 0.56
A) 0.89 ounces
B) 0.92 ounces
C) 1.35 ounces
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7)
D) 0.85 ounces
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the mean, median, mode, and midrange for each of the two samples, then compare the two sets of results.
8) The Body Mass Index (BMI) is measured for a random sample of men and women.
8)
Interpret the results by determining whether there is a difference between the two data
sets that is not apparent from a comparison of the measures of center. If there is, what is it?
24 23.5 20 27 29 22.5 28 24
Men
Women 18 20 24 25 27 21 22 25
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the mean of the data summarized in the given frequency distribution.
9) The test scores of 40 students are summarized in the frequency distribution below. Find the mean
score.
9)
Score Students
50-59
11
60-69
8
70-79
7
80-89
8
90-99
6
A) 68.4
B) 74.5
C) 64.8
D) 72.0
Find the range for the given data.
10) Fred, a local mechanic, gathered the following data regarding the price, in dollars, of an oil and
filter change at twelve competing service stations:
32.95 24.95 26.95 28.95
18.95 28.95 30.95 22.95
24.95 26.95 29.95 28.95
Compute the range.
A) $10
B) $8
C) $12
D) $14
Find the variance for the given data. Round your answer to one more decimal place than the original data.
11) 7, 6, 14, 14, and 7
A) 16.2
B) 35.5
C) 16.3
11)
D) 13.0
12) The weights (in ounces) of 10 cookies are shown.
0.75 0.72 1.14 0.7 1.36
1.15 1.27 0.96 0.59 0.82
Compute the variance.
A) 0.054
10)
12)
B) 0.065
C) 0.072
D) 0.059
Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
13) 496, 598, 503, 528, 565, 601, 576, 543
13)
A) 40.4
B) 182.1
C) 170.2
2
D) 60.6
14) To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a
specific model. The prices he was quoted are listed below:
$177 $375 $261 $408 $218 $345 $313 $318
Compute the standard deviation s.
A) $729,028.1
B) $78.5
C) $772,181.0
D) $268.0
Solve the problem.
15) The heights in feet of people who work in an office are as follows. Use the range rule of thumb to
find the standard deviation. Round results to the nearest tenth.
5.6 6.1 5.9 5.4 6.1 6.0 6.1 6.2 5.9 6.0
A) 1.2
B) 0.2
C) 0.1
Use the empirical rule to solve the problem.
17) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a
standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure
between 96 mmHg and 144 mmHg?
B) 99.7%
C) 68%
B) -20
C) 2
C) 3.4, no
18)
D) 20
19) The mean height of a basketball team is 6 feet with a standard deviation of 0.2 feet. The teamʹs
center is 6.8 feet tall. Find the centerʹs z score. Is his score unusual?
B) 3.5, no
17)
D) 99.99%
Solve the problem. Round results to the nearest hundredth.
18) Scores on a test have a mean of 67 and a standard deviation of 10. Michelle has a score of 87.
Convert Michelleʹs score to a z-score.
A) 4, yes
16)
B) 16.07 ounces, 16.17 ounces
D) 16.12 ounces, 16.48 ounces
A) 16.21 ounces, 16.39 ounces
C) 16.03 ounces, 16.57 ounces
A) -2
15)
D) 0.5
16) A company performs quality control on its juice bottles. It finds that the volumes of juice in its 16
ounce bottles have a mean of 16.3 ounces and a standard deviation of 0.09 ounces. Use the range
rule of thumb to estimate the minimum and maximum ʺusualʺ volumes.
A) 95%
14)
19)
D) 4.4, yes
Find the z-score corresponding to the given value and use the z -score to determine whether the value is unusual.
Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth
if necessary.
20) A body temperature of 99.9° F given that human body temperatures have a mean of 98.20 ° F and a 20)
standard deviation of 0.62°.
A) 2.8; unusual
C) -2.8; unusual
B) 1.7; not ususal
D) 2.8; not unusual
3
Determine which score corresponds to the higher relative position.
21) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score
of 688 on a test with a mean of 493 and a standard deviation of 150?
21)
A) A score of 688
B) A score of 92
C) Both scores have the same relative position.
Find the indicated measure.
22) The weights (in pounds) of 30 newborn babies are listed below. Find P16.
22)
5.5 5.7 5.8 5.9 6.1 6.1 6.4 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
A) 4.8
B) 6.1
C) 5.9
D) 6.0
23) The test scores of 32 students are listed below. Find P46.
23)
32 37 41 44 46 48 53 55
56 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
80 82 83 86 89 92 95 99
A) 15
B) 67
C) 14.72
D) 68
Find the percentile for the data point.
24) In a data set with a range of 60.2 to 108.9 and 300 observations, there are 207 data points with
values less than 92.4. Find the percentile for 92.4.
A) 644
B) 32
C) 69
D) 117.86
25) Data set: 20 30 70 40 20 50 90 90 110 30 30 90 60 10 90;
data point 70
A) 35
B) 70
25)
C) 52
D) 60
Provide an appropriate response.
26) Human body temperatures have a mean of 98.20 ° F and a standard deviation of 0.62°. Sallyʹs
temperature can be described by z = -1.9. What is her temperature? Round your answer to the
nearest hundredth.
A) 96.30°F
B) 97.02°F
C) 99.38°F
B) False
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26)
D) 95.14°F
27) If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores
will be bell-shaped regardless of the distribution of the original data. True or false?
A) True
24)
27)
Construct a boxplot for the given data. Include values of the 5 -number summary in all boxplots.
28) The weights (in pounds) of 30 newborn babies are listed below. Construct a boxplot for the data
set.
28)
5.5 5.7 5.8 5.9 6.1 6.1 6.3 6.4 6.5 6.6
6.7 6.7 6.7 6.9 7.0 7.0 7.0 7.1 7.2 7.2
7.4 7.5 7.7 7.7 7.8 8.0 8.1 8.1 8.3 8.7
A)
B)
C)
D)
29) The highest temperatures ever recorded (in °F) in 32 different U.S. states are shown below.
Construct a boxplot for the data set.
100 100 105 105 106 106 107 107
109 110 110 112 112 112 114 114
114 115 116 117 118 118 118 118
118 119 120 121 122 125 128 134
A)
B)
C)
D)
5
29)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
30) In the Florida lottery, the numbers (between 1 and 49) are generated randomly with the
expectation that each number has an equal chance of winning. Draw a boxplot which
should illustrate the data set of all numbers picked for the lottery during the past year.
30)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct a modified boxplot for the data.
31) The weights (in ounces) of 27 tomatoes are listed below. Construct a modified boxplot for the data.
1.7 2.0
2.6 2.6
2.9 2.9
A)
2.2
2.7
3.0
2.2
2.7
3.0
2.4
2.7
3.1
2.5
2.8
3.1
2.5
2.8
3.3
2.5
2.8
3.6
2.6
2.9
4.2
B)
C)
D)
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31)
Answer Key
Testname: CH 3 SET 1
1)
2)
3)
4)
5)
6)
7)
8)
Answers will vary.
Answers will vary.
Answers will vary.
Answers will vary.
B
B
B
Men: 24.75; 24; 24; 24.5
Women: 22.75; 23; 25; 22.5
The measures of the center for the men are much closer together.
9) D
10) D
11) C
12) C
13) A
14) B
15) B
16) D
17) A
18) C
19) A
20) A
21) B
22) B
23) D
24) C
25) D
26) B
27) B
28) A
29) D
30) Answers will vary.
31) B
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