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AP Statistics - OVD: One-Variable Data

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1 Exploratory Analysis > One-variable data analysis · Level 3
One element in the dotplot above is labeled X. Which of the statements below is true?
문제 이미지
A
X has the smallest z-score, in absolute value, of any element in the set.
B
X has the largest z-score, in absolute value, of any element in the set.
C
X has the smallest value of any element in the set.
D
A boxplot will plot X as an isolated point.
E
A back-to-back stemplot will show two symmetric clusters.
2 Exploratory Analysis > One-variable data analysis · Level 3
The histogram shown above might correspond to which of the boxplots below?
문제 이미지
A
Choice A
B
Choice B
C
Choice C
D
Choice D
E
Choice E
3 Exploratory Analysis > One-variable data analysis · Level 3
All students at a private middle school are required to sign up for one of the three clubs: chess, drama, or math. The graph below shows the distribution of participation by grade level. Which of the following statements is incorrect?
문제 이미지
A
30 percent of the 6th graders joined the math club.
B
The number of 8th graders who joined the chess club is the same as the number of 8th graders who joined the math club.
C
The number of 6th graders who joined the drama club is the same as the number of 7th graders who joined the drama club.
D
The percent of 8th graders who joined the math club is twice the percent of 7th graders who joined the math club.
E
The percent of 6th graders who joined the chess club is the same as the percent of 8th graders who joined the drama club.
4 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following is a true statement about stemplots?
A
Stemplots are equally useful for small and for very large data sets.
B
Stemplots are useful both for quantitative and for categorical data sets.
C
Stemplots can show symmetry, gaps, clusters, and outliers.
D
Stems should be skipped only if there is no data value for a particular stem.
E
Whether or not to provide a key depends on the relative importance of the data.
5 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following is incorrect?
A
In histograms, frequencies can be determined from relative heights.
B
In histograms, relative areas correspond to relative frequencies.
C
Boxplots, dotplots, stemplots, and histograms can all show skewness.
D
Sets with different distribution shapes can have identical boxplots.
E
Both dotplots and stemplots can show symmetry, gaps, clusters, and outliers.
6 Exploratory Analysis > One-variable data analysis · Level 3
If three stations are selling gas for \$2.10 per gallon, six are selling gas for \$2.05 per gallon, and ten are selling gas for \$2.00 per gallon, what is the median price per gallon among these stations?
A
\$2.00
B
\$2.025
C
\$2.0316
D
\$2.05
E
\$2.075
7 Exploratory Analysis > One-variable data analysis · Level 3
Suppose the average score of a national exam is 1,000 with a standard deviation of 200. If each score is increased by 50 and then each result is increased by 5 percent, what are the new mean and standard deviation?
A
\(\mu = 1{,}100\) and \(\sigma = 200\)
B
\(\mu = 1{,}100\) and \(\sigma = 210\)
C
\(\mu = 1{,}102.5\) and \(\sigma = 200\)
D
\(\mu = 1{,}102.5\) and \(\sigma = 210\)
E
\(\mu = 1{,}102.5\) and \(\sigma = 212.5\)
8 Exploratory Analysis > One-variable data analysis · Level 3
For which of the following variables would it be most appropriate to construct a histogram?
A
Television brand
B
Insect species
C
Gender
D
Eye color
E
Phone call length
9 Exploratory Analysis > One-variable data analysis · Level 3
If the standard deviation of a set of observations is 0, you can conclude
A
that a mistake in arithmetic has been made
B
that there is no relationship among the observations
C
that the average value is 0
D
that all observations are the same value
E
none of the above
10 Exploratory Analysis > One-variable data analysis · Level 3
To which of the histograms below can the following boxplot correspond?
문제 이미지
A
Choice A
B
Choice B
C
Choice C
D
Choice D
11 Exploratory Analysis > One-variable data analysis · Level 3
Given that the median of a set is 350 and the interquartile range is 50, which of the following statements is true?
A
Fifty percent of the data are less than or equal to 350.
B
Fifty percent of the data are between 325 and 375.
C
Seventy-five percent of the data are less than or equal to 375.
D
The mean is between 325 and 375.
E
All of the above statements are true.
12 Exploratory Analysis > One-variable data analysis · Level 3
The 15 tenure track professors in a university math department are paid an average of \$90,000 per year, while the 10 adjunct professors are paid an average of \$60,000 per year. What is the average salary among all these math professors?
A
\$72,000
B
\$75,000
C
\$78,000
D
\$81,000
E
\$84,000
13 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following statements about histograms is true?
A
Two students working with the same set of data may come up with histograms that look different.
B
Histograms of categorical variables can pinpoint clusters and gaps.
C
Unlike other graphs, histogram axes do not need to be labeled.
D
Displaying outliers is less problematic when using histograms than when using stemplots.
E
Histograms are more widely used than stemplots or dotplots because histograms display the values of individual observations.
14 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following statements about the above two dotplots is true?
문제 이미지
A
The mean of set A looks to be greater than the mean of set B.
B
The mean of set B looks to be greater than the mean of set A.
C
Both sets have roughly the same variance.
D
The empirical rule applies only to set A.
E
The standard deviation of set B is less than 4.
15 Exploratory Analysis > One-variable data analysis · Level 3
Students who apply for graduate school usually must take the GRE exam. The following boxplots were constructed from GRE quantitative scores (which take values between 130 and 170) of men and women at a state college. Which of the following is a possible boxplot for the combined score of all the students?
문제 이미지
A
Choice A
B
Choice B
C
Choice C
D
Choice D
E
Choice E
16 Exploratory Analysis > One-variable data analysis · Level 3
The histograms below give the heights of players in two amateur basketball leagues. Which one of the following statements is true?
문제 이미지
A
The distribution of heights in League A has a lower mean and lower range than the distribution of heights in League B.
B
The distribution of heights in League A has a lower mean and approximately the same range as the distribution of heights in League B.
C
The distribution of heights in League A has a higher mean and lower range than the distribution of heights in League B.
D
The distribution of heights in League A has a higher mean and higher range than the distribution of heights in League B.
E
The distribution of heights in League A has a higher mean and approximately the same range as the distribution of heights in League B.
17 Exploratory Analysis > One-variable data analysis · Level 3
Given these parallel boxplots, which of the statements below is incorrect?
문제 이미지
A
The ranges are the same.
B
The interquartile ranges are the same.
C
Both sets have left and right skews.
D
It is possible that set A does not have a symmetric or even a roughly symmetric distribution.
E
It is possible that set A has 1,000 times as many values as set B.
18 Exploratory Analysis > One-variable data analysis · Level 3
Suppose the scores on an exam have a mean of 80 with a standard deviation of 5. If one student has a test result with a z-score of –1.4 and a second student has a test result with a z-score of 2.6, how many points higher was the second student's result than that of the first?
A
6
B
7
C
13
D
19
E
20
19 Exploratory Analysis > One-variable data analysis · Level 3
Each of the high school students in a random sample was given five minutes to solve as many short puzzles as possible. The results by gender are given in the dotplots below. Which of the following is a true statement?
문제 이미지
A
One distribution is roughly symmetric; the other is skewed right.
B
The difference in their means is less than the difference in their medians.
C
The ranges are both 6.
D
The standard deviations are roughly the same.
E
The range of the entire set of results is equal to the sum of the individual ranges of the two gender specific sets.
20 Exploratory Analysis > One-variable data analysis · Level 3
A business magazine plans to compare the entry-level salaries offered to applicants with and without an MBA degree. Which of the following graphical displays is inappropriate?
A
Side-by-side histograms
B
Back-to-back stemplot
C
Parallel boxplots
D
Scatterplot
E
All of the above displays are appropriate.
21 Exploratory Analysis > One-variable data analysis · Level 3
Given this back-to-back stemplot, which of the following statements is incorrect?
문제 이미지
A
The distributions have the same mean.
B
The distributions have the same interquartile range.
C
The distributions have the same range.
D
The distributions have the same standard deviation.
E
The distributions have the same variance.
22 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following statements about the range is incorrect?
A
The range is a single number, not an interval of values.
B
Although the range is affected by outliers, the interquartile range is not.
C
The interquartile range is the range of the middle half of the data.
D
Changing the order from ascending to descending changes the sign of the range.
E
The range of the sample data can never be greater than the range of the population.
23 Exploratory Analysis > One-variable data analysis · Level 3
A college statistics professor gives only two exams during the semester, a midterm and a final. The professor grades with z-scores. On the final exam, a student received a grade of -2.8. What is the correct interpretation of this grade?
A
The student scored 2.8 points lower on the final than on the midterm.
B
The student scored 2.8 points lower than the class average on the final.
C
The student scored 2.8 standard deviations lower on the final than on the midterm.
D
The student scored 2.8 standard deviations lower on the final than the class average on the midterm exam.
E
The student scored 2.8 standard deviations lower on the final than the class average on the final exam.
24 Exploratory Analysis > One-variable data analysis · Level 3
Given the two histograms above, which of the following statements is incorrect?
문제 이미지
A
As long as the sample sizes are at least 30, the empirical rule applies to both sets.
B
Both sets have roughly the same ranges.
C
The standard deviation of set A is greater than 5.
D
The standard deviation of set B is greater than 5.
E
A lower percentage of the values in set A are at least 10 units from its mean than is the case for set B.
25 Exploratory Analysis > One-variable data analysis · Level 3
Given the cumulative frequency plot above, what is the value of the mean?
문제 이미지
A
The mean is between 75 and 80.
B
The mean is between 70 and 75.
C
The mean equals 70.
D
The mean is less than 70.
E
From such a plot, one can determine the median, but nothing can be concluded about the mean.
26 Exploratory Analysis > One-variable data analysis · Level 3
A random sample of scores at a bowling alley one day gives the following summary statistics: \(n = 26\), \(\overline{x} = 132.34\), \(s = 10.18\), \(\min = 113\), \(Q_1 = 126\), \(\text{\med} = 134.5\), \(Q_3 = 139\), and \(\max = 160\) How many outliers are there?
A
0
B
1
C
2
D
At least 1
E
At least 2
27 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following distributions has a mean of 75 and a standard deviation of approximately 5?
A
Choice A
B
Choice B
C
Choice C
D
Choice D
E
Choice E
28 Exploratory Analysis > One-variable data analysis · Level 3
Assuming that weights of sumo wrestlers follow a bell-shaped distribution, how are the weights of the following wrestlers arranged in ascending order? I. A weight with a z-score of 1 II. A weight with a percentile rank of 80 percent III. A weight at the third quartile
A
I, II, III
B
I, III, II
C
II, I, III
D
III, I, II
E
III, II, I
29 Exploratory Analysis > One-variable data analysis · Level 3
A set has 10 outliers. If every value of this set is increased by 5 percent, how many outliers will there now be?
A
Fewer than 10
B
10
C
11
D
More than 11
E
It is impossible to determine without further information.
30 Exploratory Analysis > One-variable data analysis · Level 3
The distribution of the cost of a family's dine-out meal has a mean of \$55.30 and a standard deviation of \$4.00. If they always tip \$5 plus 10 percent of the meal, what are the mean and standard deviation of the distribution of tips?
A
Mean = \(5.00 and standard deviation = \)0.40
B
Mean = \(5.40 and standard deviation = \)4.40
C
Mean = \(5.53 and standard deviation = \)0.40
D
Mean = \(10.53 and standard deviation = \)0.40
E
Mean = \(10.53 and standard deviation = \)4.40
31 Exploratory Analysis > One-variable data analysis · Level 3
Male elk living in the wild have a mean weight of 720 pounds with a standard deviation of 32 pounds. Female elk living in the wild have a mean weight of 515 pounds with a standard deviation of 20 pounds. What is the weight of a male elk with the same standardized score (z-score) as a female elk with a weight of 500 pounds?
A
696 pounds
B
704 pounds
C
705 pounds
D
735 pounds
E
752 pounds
32 Exploratory Analysis > One-variable data analysis · Level 3
A psychology student measures the times each of five mice takes to solve a maze and reach the food reward. Which of the following statistics are probably most useful in describing the distribution of the five times?
A
Mean and standard deviation
B
Mean and variance
C
Mean and interquartile range
D
Median and standard deviation
E
Median and interquartile range
33 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following is a true statement?
A
All symmetric bell-shaped curves are normal.
B
All symmetric histograms have single peaks.
C
All normal curves are bell-shaped and symmetric.
D
If the mean equals the median, the distribution is symmetric.
E
None of the above are true statements.
34 Exploratory Analysis > One-variable data analysis · Level 3
The age distribution of 343 students who attended a hip-hop concert is shown below. Which of the following could be the median age?
문제 이미지
A
15.8
B
16.5
C
17.1
D
18.2
E
18.5
35 Exploratory Analysis > One-variable data analysis · Level 3
Given this cumulative plot of the number of Instagram pictures sent in a week by the students in an AP Art class and using the most commonly accepted definition of outliers, what numbers of Instagram pictures are considered outliers?
문제 이미지
A
Between 20 and 25
B
Between 20 and 30
C
Between 20 and 40
D
Between 20 and 25, or between 55 and 60
E
Between 20 and 30, or between 50 and 60
36 Exploratory Analysis > One-variable data analysis · Level 3
If a distribution is perfectly symmetric, which of the following must be true?
A
The distribution is uniform.
B
The mean and median are equal.
C
The interquartile range is equal to twice the standard deviation.
D
The range is twice the interquartile range.
E
The range is equal to six times the standard deviation.
37 Exploratory Analysis > One-variable data analysis · Level 3
Given the histogram above, what values would be considered outliers?
문제 이미지
A
Values between 51 and 57
B
Values between 55 and 57
C
Values between 19 and 20, and values between 50 and 57
D
Values between 19 and 25, and values between 45 and 57
E
No value is an outlier.
38 Exploratory Analysis > One-variable data analysis · Level 3
On a large campus, 500 students were surveyed about their belief in an afterlife. The following table shows their responses categorized by class.
Believe in Afterlife Do Not Believe in Afterlife
Freshmen 95 30
Sophomores 87 29
Juniors 76 51
Seniors 35 97
Of the following graphical displays, which is the most appropriate to compare the proportions of students in each class who believe in an afterlife?
A
Back-to-back stemplot
B
Parallel boxplots
C
Scatterplot
D
Segmented bar chart
E
Cumulative frequency plot
39 Exploratory Analysis > One-variable data analysis · Level 3
If quartiles \(Q_1 = 25\) and \(Q_3 = 45\), which of the following must be true?
A
The median is 35.
B
The mean is between 25 and 45.
C
The standard deviation is at most 20.
D
The range must be greater than 20.
E
None must be true.
40 Exploratory Analysis > One-variable data analysis · Level 3
A data set includes two outliers, one at each end. If both these outliers are removed, which of the following is a possible result?
A
Both the mean and median remain unchanged.
B
Both the mean and standard deviation remain unchanged.
C
Both the median and standard deviation remain unchanged.
D
Both the mean and standard deviation increase.
E
Both the median and standard deviation decrease.
41 Exploratory Analysis > One-variable data analysis · Level 3
The histogram shown above is of 52 test scores. Which of the following statements is true?
문제 이미지
A
The median score was 75.
B
If 60 and below is failing, most students failed.
C
More students scored above 80 than below 60.
D
More students scored below the median than above the median.
E
The mean score is probably greater than the median score.
42 Exploratory Analysis > One-variable data analysis · Level 3
The following parallel boxplots show the birth weights during one month at four hospitals. Average birth weight is considered to be seven pounds (112 ounces). In which hospital were a greater number of newborns born weighing between 102 and 122 ounces?
문제 이미지
A
A
B
B
C
C
D
D
E
There is insufficient information to answer.
43 Exploratory Analysis > One-variable data analysis · Level 3
Counts of the numbers of spam messages received by a company's executives during one week are summarized below.
Values Under \(Q_1\) \(Q_1\) Median \(Q_3\) Values Over \(Q_3\)
7, 9, 10 15.5 20 21.5 28, 30, 31
How many outliers are there?
A
0
B
1
C
2
D
4
E
6
44 Exploratory Analysis > One-variable data analysis · Level 3
Which of the following is a true statement?
A
If the mean and median of a set are equal, then the variance is zero.
B
If a set has variance zero, then the mean, median, and standard deviation are equal.
C
If the population mean and median are equal, then this will also be true for any sample that is randomly selected from the population.
D
If the population has variance zero, then the variance of any sample is also zero.
E
If the variance of a randomly selected sample is zero, then the population mean and median are equal.
45 Exploratory Analysis > One-variable data analysis · Level 3
When there are multiple gaps and clusters, which of the following is the best choice to give an overall picture of the distribution?
A
Mean and standard deviation
B
Mean and interquartile range
C
Boxplot with its five-number summary
D
Stemplot or histogram
E
None of the above are really helpful in showing gaps and clusters.
46 Exploratory Analysis > One-variable data analysis · Level 3
The mean length of human pregnancies is 266 days with a standard deviation of 16 days. Which of the following is the best description of the standard deviation?
A
Approximately the median time between the lengths of individual pregnancies and 266 days
B
Approximately the mean time between the lengths of individual pregnancies and 266 days
C
Approximately the square root of the mean time between the lengths of individual pregnancies and 266 days
D
One-third the time between the maximum individual length of pregnancies and 266
E
One-sixth the time between the maximum and minimum individual lengths of pregnancies
47 Exploratory Analysis > One-variable data analysis · Level 3
In which of the following histograms is the mean greater than the median?
A
Choice A
B
Choice B
C
Choice C
D
Choice D
E
Choice E
48 Exploratory Analysis > One-variable data analysis · Level 3
Ms. D teaches three sections of AP Statistics with a total of 77 students. Her students did exceptionally well on the final exam. Some summary statistics and a histogram of the exam scores are shown below.
Mean Standard Deviation \(Q_1\) \(Q_3\)
93.4 2.6 92 95
Using the standard definition of outlier, which of the following can be concluded?
문제 이미지
A
The mean is greater than the median, and there is only one outlier.
B
The mean is greater than the median, and there are two outliers.
C
The mean is less than the median, and there are no outliers.
D
The mean is less than the median, and there is only one outlier.
E
The mean is less than the median, and there are two outliers.
49 Exploratory Analysis > One-variable data analysis · Level 3
The students from each of two schools were asked how many Nobel Peace Prize winners they could name. The results are shown in the following two histograms. Which school has the greater median with regard to the number of Nobel Peace Prize winners students could name, and which school has the greater mean?
문제 이미지
A
Greater median: A Greater mean: A
B
Greater median: A Greater mean: B
C
Greater median: B Greater mean: A
D
Greater median: B Greater mean: B
E
Greater median: B Equal means
50 Exploratory Analysis > One-variable data analysis · Level 3
In 1999, NASA lost the \$125 million Mars Climate Orbiter spacecraft after a 286-day journey to Mars. Miscalculations due to the use of English units instead of metric units apparently sent the craft off course. Suppose a particular measurement from a set of measurements in miles has a \(z\)-score of 0.85. If all the measurements are converted to kilometers, w hat will now be the \(z\)-score of the particular measurement? (Remember that 1 kilometer equals 0.621 miles.)
A
0.85
B
0.85 miles
C
0.85 kilometers
D
\((0.85)(0.621)\)
E
\(0.85 + 0.621\)
51 Exploratory Analysis > One-variable data analysis · Level 3
The prices at which a particular AP Statistics review book are sold at 92 online sites are summarized in the table below. Which of the following best describes the distribution of prices?
A
Roughly normal
B
Skewed left
C
Skewed right
D
Skewed both left and right
E
Bimodal
52 Exploratory Analysis > One-variable data analysis · Level 3
Given the back-to-back stemplot above, which of the following statements is true?
문제 이미지
A
The empirical rule applies to both sets A and B.
B
The median of each set is approximately \(\dfrac{500+550}{2}\).
C
The ranges of the two sets are equal.
D
The variances of the two sets are approximately the same.
E
In one set, the mean and median should be about the same. In the other set, the mean appears to be greater than the median.
53 Exploratory Analysis > One-variable data analysis · Level 3
The following histogram displays the top speeds of several roller coasters. Which of the following statements must be true?
문제 이미지
A
The minimum and maximum top speeds are 30 mph and 100 mph, respectively.
B
The median top speed is 60.5 mph.
C
At least 100 more roller coasters have top speeds between 70 and 80 mph than between 30 and 40 mph.
D
More roller coasters have top speeds between 70 and 80 than have top speeds over 80 mph.
E
The same number of roller coasters have top speeds between 50 and 60 mph as have top speeds between 80 and 90 mph.
54 Exploratory Analysis > One-variable data analysis · Level 3
Summary statistics for the number of campsites at public parks in a large western state are as follows.
Minimum Q₁ Median Q₃ Maximum Mean Standard Deviation
0 35 61 95 300 73.2 58
A check of the data shows that 5 had been subtracted from every value to bring the minimum to 0 for some calculation purpose. If 5 is added back to every value, what will now be the interquartile range and the standard deviation?
A
IQR = 60 and SD = 58
B
IQR = 60 and SD = 63
C
IQR = 65 and SD = 58
D
IQR = 65 and SD = 63
E
IQR = 62.5 and SD = 60.5
55 Exploratory Analysis > One-variable data analysis · Level 3
Below are histograms of two data sets. Which of the following statements must be true?
문제 이미지
A
The medians of the two data sets must be equal.
B
The means of the two data sets must be equal.
C
The ranges of the two data sets must be equal.
D
The standard deviation of data set S is less than the standard deviation of data set T.
E
The standard deviation of data set S is greater than the standard deviation of data set T.
56 Exploratory Analysis > One-variable data analysis · Level 3
A study of phone, e-mail, and texting communication in three time periods results in the following segmented bar chart. Which of the following is greatest?
문제 이미지
A
The number of texts and e-mails in 2010.
B
The number of e-mails in 2014.
C
The number of texts in 2018.
D
The above are all equal.
E
It is impossible to answer this question without knowing the actual numbers of individual communications involved.
57 Exploratory Analysis > One-variable data analysis · Level 3
A normal distribution with mean 25 and standard deviation 5 is standardized by subtracting the mean from each value and dividing the difference by the standard deviation. What are the mean and standard deviation of the resulting distribution?
A
Mean = 0, Standard deviation = 1
B
Mean = 5, Standard deviation = 1
C
Mean = 5, Standard deviation = 5
D
Mean = 25, Standard deviation = 1
E
Mean = 25, Standard deviation = 5
58 Exploratory Analysis > One-variable data analysis · Level 3
A barber measures hair lengths for a random sample of 100 of his customers and gathers data on the growth rates of their hair. The data are plotted in the histogram below. Which of the values below is closest to the standard deviation of the 100 values?
문제 이미지
A
0.008
B
0.01
C
0.03
D
0.08
E
1.16
59 Exploratory Analysis > One-variable data analysis · Level 3
A teacher had two AP Statistics classes. The mean score on the AP Exam for one class was 3.2, while the mean score for the other class, which had more students, was 3.8. What must be true about the mean score of all of the teacher's AP students?
A
The mean score for all students must be 3.5.
B
It's possible that the mean score of all students is 3.5, but it doesn't have to be.
C
The mean score for all students can be anything between 3.2 and 3.8.
D
The mean score for all students is less than 3.5 but greater than 3.2.
E
The mean score for all students is greater than 3.5 but less than 3.8.
60 Exploratory Analysis > One-variable data analysis · Level 3
Consider the three distributions below. Order the distributions from least to greatest in terms of the proportion of data less than the mean.
문제 이미지
A
M, L, N
B
N, L, M
C
M, N, L
D
N, M, L
E
L, N, M
61 Exploratory Analysis > One-variable data analysis · Level 3
The following statistics summarize the fuel economy in miles per gallon (mpg) for 50 different car models in 2018.
Minimum Q₁ Median Q₃ Maximum Mean Standard Deviation
13.5 21 24.5 30 48.5 26 7.32
Which of the following is a true statement?
A
50 percent of the mpg values are between 26 and 48.5.
B
25 percent of the mpg values are above 21.
C
The distribution of mpg values appears to be roughly bell-shaped.
D
The interquartile range of mpg values is 5.
E
There is at least one outlier.
62 Exploratory Analysis > One-variable data analysis · Level 3
College students' expenses for academic supplies have a mean of \$1,100 and a standard deviation of \$290. Their expenses for entertainment have a mean of \$950 and a standard deviation of \$250. Assuming the expenses for academic supplies and for entertainment are independent, what are the mean and standard deviation of the total yearly expenditures by college students for these two items?
A
Mean = \(1025 and standard deviation = \)270
B
Mean = \(1025 and standard deviation = \)383
C
Mean = \(2050 and standard deviation = \)270
D
Mean = \(2050 and standard deviation = \)383
E
Mean = \(2050 and standard deviation = \)540
63 Exploratory Analysis > One-variable data analysis · Level 3
Random samples are taken from three populations, and the resulting parallel boxplots of the data follows. Which of the following statements is true?
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A
One of the sample distributions is roughly a normal distribution.
B
All three sample distributions have the same interquartile range.
C
All three sample distributions have the same range.
D
All three sample medians are between 11 and 15.
E
All three of the distributions can reasonably be assumed to be of samples from populations with roughly normal distributions.
64 Exploratory Analysis > One-variable data analysis · Level 3
A histogram of the educational level (in number of years of schooling) of the adult population of the United States would probably have which of the following characteristics?
A
A roughly normal population
B
Skewness to the right
C
Symmetry
D
A gap around 12 years
E
Clusters around 8, 12, and 16 years
65 Exploratory Analysis > One-variable data analysis · Level 3
When a set of data has suspect outliers, which of the following are preferred measures of central tendency and variability?
A
Mean and standard deviation
B
Mean and variance
C
Mean and range
D
Median and range
E
Median and interquartile range
66 Exploratory Analysis > One-variable data analysis · Level 3
Data were collected as to the magnitudes of earthquakes in a certain region over a long time period. Based on the boxplot above, which of the following is a reasonable conclusion about earthquake magnitudes in that region during that time period?
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A
The distribution is roughly normal.
B
The distribution is symmetric.
C
There were a greater number of earthquakes with magnitudes below 6 than between 6 and 6.75.
D
There were the same number of earthquakes between the median and the third quartile magnitudes as there were between the third quartile and the maximum magnitudes.
E
Over half the earthquakes had magnitudes between 6 and 7.5.
67 Exploratory Analysis > One-variable data analysis · Level 3
Suppose the height distribution of male college basketball players is approximately normal and varies from 71 to 81 inches, while the height distribution of female college basketball players is approximately normal and varies from 65 to 72 inches. A random stratified sample of 500 male and 500 female college basketball players is then combined into one large sample of size 1,000. What is the distribution of this sample?
A
Roughly normal, varying from 65 to 81 inches and centered at 71.5 inches
B
Roughly uniform
C
Unimodal and symmetric but not normal
D
Skewed
E
Bimodal
68 Exploratory Analysis > One-variable data analysis · Level 3
A company reports mean salaries cross-classified by position and gender.
Male Female
Junior Executives $45000 \$48,000
Senior Executives $93000 \$95,000
Overall ? ?
Is it possible that males have an overall higher mean salary than females?
A
No, because \(\dfrac{45000+93000}{2} < \dfrac{48000+95000}{2}\)
B
No, because female junior executives have a higher mean salary than male junior executives and female senior executives have a higher mean salary than male senior executives
C
No, because \(n(48000 - 45000) + m(95000 - 93000) > 0\) for all \(n\) and \(m\)
D
Yes, depending on the number of males and females who are junior and senior executives
E
Yes, because salaries are a numerical, not a categorical, variable
69 Exploratory Analysis > One-variable data analysis (FR) · Level 3
In a random sample of 20 high school students, the number of text messages sent by each during the past day were {0, 4, 8, 12, 13, 15, 15, 18, 23, 24, 40, 43, 47, 50, 53, 57, 59, 61, 61, 65}. (a) Create a stemplot of the number of text messages sent by students. (b) Describe the distribution. (c) Would a boxplot give more, less, or basically the same information? Explain.
70 Exploratory Analysis > One-variable data analysis (FR) · Level 3
The histogram below shows the distribution of weights of the 21 bags of candy coming off an assembly line during a one-minute production interval. (a) Write a few sentences to describe the distribution of bag weights for the one-minute interval. (b) One of the bag weights is 15.85 ounces. If this bag weighed 15.75 ounces instead of 15.85 ounces, what effect would the decrease have on the mean and on the median?
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71 Exploratory Analysis > One-variable data analysis (FR) · Level 3
A bank cybersecurity engineer notes the number of malware intrusions intercepted each hour during a random sample of 109 hour-long periods. (a) Describe the distribution. (b) Is the quotient, \(\dfrac{\text{mean intrusions}}{\text{median intrusions}}\), greater than 1, less than 1, or approximately 1? Explain. (c) Are conditions for inference (constructing a confidence interval for the mean number of intrusions per hour) met? Explain.
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72 Exploratory Analysis > One-variable data analysis (FR) · Level 3
Do graduates from different universities obtain different starting salaries? In one study of starting salaries, random samples of graduates from two universities were surveyed and their starting salaries noted. The histograms below display the data. (a) Compare the distributions of starting salaries of graduates from the two universities. (b) Which is greater, the difference between the two university mean starting salaries or the difference between the two university median starting salaries? Explain.
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73 Exploratory Analysis > One-variable data analysis (FR) · Level 3
In independent random samples of 20 high school students and 20 college students, each student gave a rating between 0 and 100 for a new music website. HS students: 27, 32, 82, 36, 43, 75, 45, 16, 23, 48, 51, 57, 60, 64, 39, 40, 69, 72, 54, 57 College students: 49, 50, 35, 69, 75, 35, 49, 54, 98, 58, 22, 34, 60, 38, 47, 65, 79, 38, 42, 87 Using back-to-back stemplots, compare the distributions.
74 Exploratory Analysis > One-variable data analysis (FR) · Level 3
The A1C test is used to diagnose diabetes. Cumulative graphs of A1C level readings in the populations of three countries (A, B, and C) are given below. Write a few sentences comparing the distributions of A1C level readings in the three countries.
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75 Exploratory Analysis > One-variable data analysis (FR) · Level 3
Ms. D. has 12 students in her AP Statistics class. They all did very well on the final exam with scores of {81, 87, 88, 88, 88, 89, 89, 90, 90, 90, 90, 95}. (a) The trimean is defined as \(\dfrac{Q_1 + 2\text{Med} + Q_3}{4}\). Compute the trimean for the above data. Show your work. (b) The mean trimmed 50% is computed by trimming the upper 25% of the scores and the lower 25% of the scores and then computing the mean of the remaining scores. Compute the mean trimmed 50% for the above data. Show your work. (c) More generally, to compute a trimmed mean, you remove some of the higher and lower scores and then compute the mean of the remaining scores. In what way can the median be considered a trimmed mean? (d) In general, what advantage might both the trimean and a trimmed mean have over using the standard mean, \(\overline{x} = \dfrac{\sum x}{n}\)?
76 Exploratory Analysis > One-variable data analysis (FR) · Level 3
Suppose we calculate the melting points of 10 nuggets claimed to be pure silver and find the mean to be 1,760°F with a standard deviation of 27°F. (a) What would be the mean and standard deviation of the melting points of the 10 nuggets if the 10 measurements were converted to Celsius? (°F = (1.8)(°C) + 32) (b) How would the conversion above have changed if the sample size had been 20 nuggets instead of 10 nuggets?
77 Exploratory Analysis > One-variable data analysis (FR) · Level 3
The mean absolute deviation (MAD) of a set \(\{x_1, ..., x_n\}\) is defined to be \(\text{MAD} = \dfrac{1}{n}\displaystyle\sum_{i=1}^n|x_i - \overline{x}|\). (a) Compare the MADs of the sets with the two dotplots. (b) After comparing the above answers, is this what was expected?
78 Exploratory Analysis > One-variable data analysis (FR) · Level 3
Consider the following dotplot of 21 values. (a) Calculate and compare the mean and median. (b) Comment on whether your answer was as expected.
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79 Exploratory Analysis > One-variable data analysis (FR) · Level 3
The selling prices of a simple random sample of 20 Florida condos is summarized below.
Price (\$1,000) 0–100 100–200 200–300 300–400 400–500
Frequency 1 0 10 5 4
(a) Draw a cumulative frequency plot of this data. (b) If given the raw data, would the mean or the median best describe the typical selling price for Florida condos? Explain.
80 Exploratory Analysis > One-variable data analysis (FR) · Level 3
Fifty subjects with advanced heart disease participated in an experiment to compare two new blood pressure medications, A and B. The subjects were randomly assigned into two groups, one group to take medication A and the other medication B. Every person's blood pressure was taken prior to assignment and again after three months on the medication. The calculated differences, old pressure minus new pressure (+ represents improvement), are shown in the following table.
Medication Values < \(Q_1\) \(Q_1\) Median \(Q_3\) Values > \(Q_3\)
A –2, –1 0 3 10 12, 15
B –2, 2 3 4 5 6, 10
(a) Draw parallel boxplots of the above data showing outliers, if any. (b) Which medication should be chosen if the goal is to have the greatest percentage of subjects lower their blood pressures? Explain. (c) Which medication should be chosen if the goal is to have the greatest mean improvement (lowering) in subjects' blood pressures? Explain.
81 Exploratory Analysis > One-variable data analysis (FR) · Level 3
The salaries of a random sample of 91 faculty members at a large university are summarized in the following histogram. (Assume salaries are at the center of each bar.) (a) Construct a boxplot of the above data. (b) What feature does the histogram show that is missed by the boxplot? (c) What feature is more clearly distinguished in the boxplot than in the histogram?
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82 Exploratory Analysis > One-variable data analysis (FR) · Level 3
It is difficult to know when a minute has passed without looking at a clock. A random sample of 18 students consisted of 11 boys and 7 girls. With eyes closed, each student raised his/her hand when he/she guessed that a minute had passed. Their times were recorded and are displayed below. (a) In either the boy or girl distributions, are any of the times considered to be outliers? Explain. (b) If all the times are combined, does the new set of times have any outliers? Explain. (c) Explain the reason for the answer to (b) in relation to the answer to (a).
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83 Exploratory Analysis > One-variable data analysis (FR) · Level 3
Two species of insects were continually genetically modified over the course of a 90-day period of time (their normal life expectancy). The resulting age (in days) and gender distributions are given in the population pyramids below. (a) In which interval is the median age of the Species B insects? Explain. (b) In either or both species, have the modifications resulted in longer life expectancies for males or females? Explain. (c) Have the most recent modifications resulted in favoring more births of a particular gender in either or both species?
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84 Exploratory Analysis > One-variable data analysis (FR) · Level 3
A furniture store sells low-end and high-end outdoor patio furniture. The selling prices ($) for their lounge chairs (low- and high-end) are summarized in the boxplots below. (a) Compare the distributions of the prices of the low- and high-end lounge chairs. (b) If a single histogram was made of all the lounge chair prices, describe its shape.
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85 Exploratory Analysis > One-variable data analysis (FR) · Level 3
A cumulative relative frequency plot for scores (maximum possible 120) on an arcade video game during one 24-hour period is as follows. (a) Interpret in context the meaning of the point (50, 0.2). (b) Can you make an estimate for the number of scores below 60? (c) What is the median score? (d) What proportion of the scores are over 80? (e) What does the flat portion between 80 and 90 mean?
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86 Exploratory Analysis > One-variable data analysis (FR) · Level 3
Cereal is the breakfast of choice for many children. Nutritional content varies widely, with dieticians saying that the best cereals are low in sugar, high in fiber, and full of protein. Nutritional content also varies widely among boxes of the same cereal. Below is summarized the nutritional content found in samples consisting of 20 boxes taken of each of three cereals, all advertised as "whole grain corn flakes." (a) Compare the fiber contents of the three cereals. (b) If you used only one measurement—sugar, fiber, or protein—to identify which of these three cereals you were analyzing, what would you choose and why? (c) If a chemical analysis of an unidentified box of one of these cereals shows a total of 30 grams of sugar, fiber, and protein per serving, which cereal would you guess you have? Explain.
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