Exercise \(\PageIndex{1}\)
A study was conducted of Long Beach School District schools regarding how many require school uniforms. In 2006, of the 296 schools questioned, 184 said they required school uniforms. (Gentile & Imberman, 2009) Find the proportion of schools that require a school uniform.
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A Center for Disease Control (CDC) study conducted in 2008, found that out of 32,601 children in Arizona, 507 had autism. (CDC, 2012) Find the proportion of children in Arizona who had autism in 2008.
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The temperatures (in degrees Fahrenheit) for the first 10 days of July 2013 in Phoenix, AZ are given in the table below ("Weather underground," 2013).
|
112
|
108
|
111
|
108
|
106
|
|
111
|
112
|
113
|
107
|
104
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
-
The number of traffic fatalities involving a driver with a blood alcohol content of 0.1 or more is given in the table for the southern states in 2013 ("Traffic fatalities by," 2013).
|
260
|
904
|
394
|
366
|
177
|
194
|
|
264
|
430
|
423
|
345
|
278
|
134
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
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A new sedan car in 2013 or 2014, which has a gas mileage in the city of 40 to 50 mpg, had the following prices ("Motor trend," 2013).
|
$38,700
|
$26,200
|
$39,780
|
$27,200
|
$38,700
|
|
$24,360
|
$39,250
|
$35,925
|
$35,555
|
$26,140
|
|
$24,995
|
$28,775
|
$24,200
|
$34,755
|
$25,990
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
-
The prices of an airline flight from New York City to Los Angeles on September 7, 2013 around 8 am, and returning September 14, 2013 are given in the table below ("Expedia," 2013).
|
$317
|
$351
|
$378
|
|
$397
|
$327
|
$334
|
|
$337
|
$383
|
$327
|
-
Find the mean, median, and mode for the data set.
-
Find the range, variance, and standard deviation for the data set.
-
Find the five-number summary and the interquartile range (IQR) for the data set.
-
Draw a box-and-whiskers plot for the data set.
-
The gas prices (in $/gallon) at all gasoline stations in Flagstaff, AZ, on July 16, 2013 are given in the table below ("Arizona gas prices," 2013).
|
3.45
|
3.47
|
3.48
|
3.48
|
3.48
|
3.49
|
|
3.51
|
3.51
|
3.51
|
3.55
|
3.55
|
3.56
|
|
3.59
|
3.59
|
3.59
|
3.59
|
3.65
|
3.65
|
|
3.65
|
3.65
|
3.66
|
3.67
|
3.69
|
3.69
|
|
3.69
|
3.69
|
3.69
|
3.69
|
3.69
|
3.69
|
|
3.69
|
|
|
|
|
|
Using a calculator, find the mean, median, standard deviation, and five-number summary.
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The city gas mileage (in mpg) of 2011 small pick-up trucks that are four-wheel drive are given in the table below ("Fuel efficiency guide," 2011).
|
17
|
18
|
17
|
14
|
16
|
16
|
|
14
|
14
|
15
|
17
|
18
|
17
|
|
14
|
16
|
16
|
14
|
14
|
15
|
|
14
|
18
|
18
|
16
|
14
|
|
Using a calculator, find the mean, median, standard deviation, and five-number summary.
-
Sustainability Victoria, in Australia, surveys all Victorian local communities on waste and recycling services every year. A random sample of 10 local communities reported the number of households served in that community in 2008 and the data is given in the table below ("2001-02 to 2007-08," 2009).
|
7,551
|
4,907
|
45,439
|
46,000
|
46,000
|
|
49,732
|
38,264
|
39,195
|
40,374
|
40,500
|
-
Find the mean and median of the data set.
-
Find the mean and the median of the data set with the two lowest data values (7,551 and 4,907) removed.
-
Discuss what happened to the mean and the median when the two lowest data values (7,551 and 4,907) are removed.
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Natural gas consumptions (in billions of cubic feet) for selected countries in South America are listed in the following table ("International energy statistics," 2013).
|
1629
|
87
|
885
|
199
|
|
312
|
8
|
202
|
961
|
-
Find the mean and median of the data set.
-
Find the mean and median with the highest data value of 1629 removed.
-
Discuss what happened to the mean and median when the highest data value (1629) is removed.
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Suppose your child takes a test to evaluate whether or not your child is at risk for Attention Deficit Hyperactivity Disorder (ADHD). One assessment for ADHD is the Behavior Assessment System for Children, Second Edition (BASC-2) survey. After taking this survey a child is rated on several different qualities. One of the qualities is aggression, where a high score represents a tendency towards being aggressive. Suppose your child is in the 35th percentile on aggression.
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What does this percentile mean?
-
What does this percentile mean about your child and this quality of ADHD?
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You are planning to go to graduate school after you finish your bachelor’s degree and you take the Graduate Record Examination (GRE). Your score on the mathematics section of the general GRE puts you in the 90th percentile.
-
What does this percentile mean?
-
Did you pass (score of 70% or better) the mathematics section of the general GRE?
-
The IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of 15. Using this information, find the following:
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What percentage of the people have IQ scores between 85 and 115?
-
What percentage of the people have IQ scores between 70 and 100?
-
What percentage of the people have IQ scores between 130 and 145?
-
What percentage of the people have IQ scores above 145?
-
The mean systolic blood pressure of people in the U.S. is 124 with a standard deviation of 16. Assume that systolic blood pressure follows a normal distribution.
-
What percentage of the people in the U.S. have systolic blood pressure between 108 and 124?
-
What percentage of the people in the U.S. have systolic blood pressure between 92 and 156?
-
What percentage of the people in the U.S. have systolic blood pressure between 76 and 108?
-
What percentage of the people in the U.S. have systolic blood pressure above 156?
-
The mean diastolic blood pressure of people in the U.S. is 77 with a standard deviation of 11. Assume that diastolic blood pressure follows a normal distribution.
-
What percentage of the people in the U.S. have diastolic blood pressure between 77 and 88?
-
What percentage of the people in the U.S. have diastolic blood pressure between 66 and 88?
-
What percentage of the people in the U.S. have diastolic blood pressure between 55 and 99?
-
What percentage of the people in the U.S. have diastolic blood pressure below 55
-
The mean height of men in the U.S. is 69.1 inches with a standard deviation of 2.9 inches. Assume that height follows a normal distribution.
-
What percentage of the males in the U.S. have height between 74.9 and 77.8 inches?
-
What percentage of the males in the U.S. have height between 60.4 and 77.8 inches?
-
What percentage of the males in the U.S. have height between 63.3 and 72 inches?
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What percentage of the males in the U.S. have heights below 63.3 inches?
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The IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of 15. Find the z-score for an IQ score of 134. Is this value unusual? Why or why not?
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The mean systolic blood pressure of people in the U.S. is 124 with a standard deviation of 16. Assume that systolic blood pressure follows a normal distribution. Find the z-score for a systolic blood pressure of 135. Is this value unusual? Why or why not?
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The mean diastolic blood pressure of people in the U.S. is 77 with a standard deviation of 11. Assume that diastolic blood pressure follows a normal distribution. Find the z-score for a diastolic blood pressure of 54. Is this value unusual? Why or why not?
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The mean height of mean in the U.S. is 69.1 inches with a standard deviation of 2.9 inches. Assume that height follows a normal distribution. Find the z-score for a man who is 64 inches tall. Is this value unusual? Why or why not?
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The IQ of a person follows a normal distribution and has a mean of 100 and a standard deviation of 15. Find the five-number summary.
-
The mean systolic blood pressure of people in the U.S. is 124 with a standard deviation of 16. Assume that systolic blood pressure follows a normal distribution. Find the five-number summary.
-
The mean diastolic blood pressure of people in the U.S. is 77 with a standard deviation of 11. Assume that diastolic blood pressure follows a normal distribution. Find the five-number summary.
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The mean height of mean in the U.S. is 69.1 inches with a standard deviation of 2.9 inches. Assume that height follows a normal distribution. Find the five-number summary.
-
It can be shown that a man’s height and a man’s weight have a positive correlation. Does this mean that a man’s height causes him to be a certain weight? Explain.
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Engine size and city gas mileage have a negative correlation. Does this mean that the engine size causes the gas mileage of a car? Explain.
-
Suppose 10 men had their height and weight measured. The data is below. Draw a scatter plot of the data. Describe what relationship you can see from the graph.
|
Height (inches)
|
67
|
72
|
74
|
65
|
70
|
72
|
74
|
69
|
68
|
70
|
|
Weight (pounds)
|
185
|
202
|
226
|
165
|
221
|
217
|
218
|
189
|
201
|
185
|
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Nine midsize 2011 hybrid cars’ city gas mileage and engine size are recorded below ("Fuel efficiency guide," 2011). Draw a scatter plot of the data. Describe what relationship you can see from the graph.
|
Engine Size
|
4.4
|
2.5
|
2.4
|
5.0
|
2.5
|
2.5
|
2.5
|
2.4
|
1.8
|
|
City MPG
|
17
|
41
|
25
|
19
|
41
|
41
|
33
|
31
|
51
|