Deck 3: Describing, Exploring, and Comparing Data

Question 1

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. Find the median number of newspapers sold.

A)202 newspapers
B)113 newspapers
C)175 newspapers
D)242 newspapers

Answer 1

A

Question 2

The customer service department of a phone company is experimenting with two different systems. On Monday they try the first system which is based on an automated menu system.
On Tuesday they try the second system in which each caller is immediately connected with a
Live agent. A quality control manager selects a sample of seven calls each day. He records the
Time for each customer to have his or her question answered. The times (in minutes)are listed below. Find the coefficient of variation for each of the two sets of data, then compare the
Variation. Round results to one decimal place. A)Automated Menu: 45.4% Live agent: 26.3%
There is substantially more variation in the times for the automated menu system.
B)Automated Menu: 48.8% Live agent: 28.3%
There is substantially more variation in the times for the automated menu system.
C)Automated Menu: 47.1% Live agent: 27.3%
There is substantially more variation in the times for the automated menu system.
D)Automated Menu: 25.2% Live agent: 41.5%
There is substantially more variation in the times for the live agent.

Answer 2

A

Question 3

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data.

A)36.1
B)4347.7
C)3999.0
D)8.35

Answer 3

D

Question 4

A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4,5,1,5,4 . The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1 , and F=0 . Compute the grade point average (GPA) and round the result to two decimal places.

A) 9.00
B) 3.46
C) 2.37
D) 1.37

Question 5

If the standard deviation for a set of data is 0, which of the following must be true?_

A)All the data values equal 0.
B)All of the data values are identical.
C)All of the data values are negative.
D)None of the above must be true since standard deviation cannot be equal to 0.

Question 6

Construct a boxplot for the given data. Include values of the 5-number summary in all_ boxplots. The test scores of 40 students are listed below.

Question 7

The prices (in dollars)of 12 electric smoothtop ranges are listed below. Find the range for the given sample data.

A)$900
B)$920
C)$930
D)$910

Question 8

The number of vehicles passing through a bank drive -up line during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going
Through the line in a 15-minute period.

A)26.85 vehicles
B)28 vehicles
C)27 vehicles
D)31 vehicles

Question 9

The test scores of 40 students are listed below. Find P56._

A)73.5
B)22.4
C)74
D)73

Question 10

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer?

A)-2.00
B)-1.00
C)0
D)2.00

Question 11

Find the standard deviation for the given sample data. Round your answer to one more_ decimal place than the original data.

A)5.1
B)5.4
C)1.6
D)5.8

Question 12

Find the variance for the given data. Round your answer to one more decimal place than the_ original data. To get the best deal on a microwave oven, Jeremy called six appliance stores
And asked the cost of a specific model. The prices he was quoted are listed below:

Question 13

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following
Choices is not true?

A)An SAT score of 1490 has a z score of -0.09.
B)An ACT score of 17.0 has a z score of -0.85.
C)The SAT score of 1490 is relatively better than the ACT score of 17.0.
D)The ACT score of 17.0 is relatively better than the SAT score of 1490.

Question 14

Find the variance for the given sample data. Round your answer to one more decimal place_ than the original data.

Question 15

Listed below are the amounts of time (in months)that the employees of a restaurant have been working at the restaurant. Find the mean for the given sample data. Round your
Answer to one more decimal place than the original data values.

A)31.5 months
B)61.1 months
C)56.7 months
D)52.9 months

Question 16

A student earned grades of 84, 78, 84, and 72 on her four regular tests. She earned a grade of_ 78 on the final exam and 86 on her class projects. Her combined homework grade was 87. The
Four regular tests count for 40% of the course grade, the final exam counts for 30%, the project
Counts for 10%, and homework counts for 20%. What is her weighted mean grade? Round to
One decimal place.

A)81.3
B)80.2
C)81.2
D)82.1

Question 17

Use the given sample data to find ._

A)67.0
B)55.0
C)6.0
D)61.0

Question 18

When finding percentiles, if the locator L is not a whole number, one procedure is to interpolate so that a locator of 23.75, for example, leads to a value that is 3/4 of the way
Between the 23rd and 24th scores. Use this method of interpolation to find P75 for the set of
Test scores below.

A)83
B)88.5
C)85.75
D)94

Question 19

Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z = -1.5. What is her temperature? Round your
Answer to the nearest hundredth.

A)97.27° F
B)99.13° F
C)96.70° F
D)95.79° F

Question 20

Approximately what percentage of apple diameters is greater than the 66th percentile?

A)66%
B)17%
C)34%
D)3.4%

Question 21

Listed below are the systolic blood pressures (in mm Hg)for a sample of men aged 20-29 years and for a sample of men aged 60-69 years. $\begin{array}{llllll}\text { Men aged 20-29: } 117 & 122 & 129 & 118 & 131 & 123 \\\text { Men aged 60-69: } 130 & 153 & 141 & 125 & 164 & 139\end{array}$
Find the coefficient of variation for each of the two sets of data, then compare the variation.
Round results to one decimal place.

A)Men aged 20-29: 4.8% Men aged 60-69: 10.6%
There is substantially more variation in blood pressures of the men aged 60-69.
B)Men aged 20-29: 4.6% Men aged 60-69: 10.2 %
There is substantially more variation in blood pressures of the men aged 60-69.
C)Men aged 20-29: 7.6% Men aged 60-69: 4.7%
There is more variation in blood pressures of the men aged 20 -29.
D)Men aged 20-29: 4.4% Men aged 60-69: 8.3%
There is substantially more variation in blood pressures of the men aged 60-69.

Question 22

The test scores of 40 students are listed below. Find P85. 6)____________ $\begin{array}{llllllllll}30 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \\59 & 62 & 63 & 65 & 66 & 68 & 69 & 69&71 & 72 \\72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \\81 & 82 & 83 & 85 & 89 & 92 & 93 & 94&97 & 98\end{array}$

A)87
B)85
C)89
D)34

Question 23

The race speeds (in minutes)for the top eight cars in a 200-mile race are listed below. Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. $\begin{array}{llllllll}181.0 & 180.6 & 189.2 & 182.2 & 175.6 & 180.0 & 177.9 & 181.8\end{array}$

A)1.1 minutes
B)6.8 minutes
C)7.5 minutes
D)3.4 minutes

Question 24

Find the standard deviation for the given sample data. Round your answer to one more decimal_ place than the original data.

A)8.35
B)3999.0
C)4347.7
D)36.1

Question 25

The mean of a set of data is 108.06 and its standard deviation is 115.45. Find the z score for a value of 489.67.

A)2.98
B)3.64
C)3.31
D)3.61

Question 26

In a data set with a range of 55.4 to 105.4 and 400 observations, there are 276 observations_ with values less than 86. Find the percentile for 86.

Question 27

Jorge has his own business as a painter. The amounts he made in the last five months are shown below:
$2426 $2463 $1451 $2154 $1119
Find the mean, median, and range of the data.

A)Mean = $1923, Median = $2154, Range = $1344
B)Mean = $2154, Median = $1923, Range = $1344
C)Mean = $1923, Median = $2154, Range = - $1344

Question 28

The local Tupperware dealers earned these commissions last month: What was the mean commission earned? Round your answer to the nearest cent.

A)$3094.01
B)$3867.52
C)$3437.79
D)$3088.01

Question 29

Last year, nine employees of an electronics company retired. Their ages (in years)at_ retirement are listed below. Find the mode(s)for the given sample data.

Question 30

A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation.

A)$7967.5
B)$7588.1
C)$8195.1
D)$8422.8

Question 31

The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.5 inches. What can you conclude from Chebyshev's theorem about the percentage of adults
In the town whose heights are between 60.1 and 74.1 inches?

A)The percentage is at most 75%.
B)The percentage is at most 95%.
C)The percentage is at least 95%.
D)The percentage is at least 75%.

Question 32

A test score of 48.4 on a test having a mean of 66 and a standard deviation of 11. Find the z_ score corresponding to the given value and use the z score to determine whether the value is
Significant. Consider a score to be significant if its z score is less than -2.00 or greater than
2.00. Round the z score to the nearest tenth if necessary.

A)-17.6; significant
B)-1.6; significant
C)-1.6; not significant
D)1.6; not significant

Question 33

Which of the following is not a property of variance?

A)The units of variance are the squares of the units of the original data.
B)The value of the variance is always positive or 0.
C)The sample variance is a biased estimator of the population variance.
D)The value of the variance is zero only when all of the data values are the same number.

Question 34

The owner of a manufacturing plant employs eighty people. As part of their personnel file, she_ asked each one to record to the nearest one-tenth of a mile the distance they travel one way
From home to work. The distances for a random sample of six employees are listed below:

Question 35

The number of hours per day a college student spends on homework has a mean of 6 hours and a standard deviation of 1.25 hours. Yesterday she spent 3 hours on homework. How
Many standard deviations from the mean is that? Round your answer to two decimal places.

A)1.20 standard deviations below the mean
B)1.20 standard deviations above the mean
C)2.40 standard deviations below the mean
D)2.40 standard deviations above the mean

Question 36

Find the variance for the given sample data. Round your answer to one more decimal place_ than the original data.

A)7.7
B)11.8
C)7.8
D)6.2

Question 37

The mean height of a basketball team is 6 feet with a standard deviation of 0.2 feet. The team's_ center is 6.9 feet tall. Find the center's z score. Is his score unusual?

A)4.95, yes
B)4.5, yes
C)3.83, no
D)4, no

Question 38

Scores on a test have a mean of 66 and a standard deviation of 9. Michelle has a score of 57._ Convert Michelle's score to a z score.

A)9
B)-1
C)1
D)-9

Question 39

How will a high outlier in a data set affect the mean and median?

A)Distribution skewed to the right, mean pulled to the right, median not effected
B)Distribution skewed to the right, mean not effected, median skewed to the right
C)Distribution skewed to the left, mean pulled to the left, median not effected
D)Distribution skewed to the right, mean not effected, median not effected

Question 40

A department store has daily mean sales of $ 28,372.72. The standard deviation of sales is $2000. On Tuesday, the store sold $34,885.21 worth of goods. Find Tuesday's z score. Was
Tuesday a significantly good day?

A)3.26, yes
B)3.42, no
C)2.61, no
D)3.57, yes

Question 41

The following are interval times (minutes)between eruptions of the Old Faithful geyser in
Yellowstone National Park (based on U.S. National Park Service data). Identify the five number summary and construct a boxplot of these data.

Question 42

Describe any similarities or differences in the two distributions represented by the following
boxplots. Assume the two boxplots have the same scale.

Question 43

Listed below are the arrival delay times (in minutes)of randomly selected flights between New
York's JFK airport to Los Angeles (LAX). Negative values correspond to flights that arrive
before their schedule time and positive values represent delays. Calculate the range of the data
and the standard deviation. Can the standard deviation be negative?

Question 44

The textbook defines significantly low or high values as those data points with z scores less
than z =−2.00 or z scores greater than z = 2.00. Comment on this definition with respect to
Chebyshev's theorem; refer specifically to the percent of scores which would be defined as
significant according to Chebyshev's theorem.

Question 45

Which do you think has less variation: the IQ scores of students in your statistics class or the
IQ scores of a simple random sample taken from the general population? Why?

Question 46

An online service ran a poll of its internet subscribers and asked whether they would re-elect
the current President. Among the 1,304,240 responses, 768,731 answered "yes", 286,756
answered "no", and 248,753 said it was "too soon to decide". Given how large this sample
is, can it be considered to be representative of the population of the United States? Explain.

Question 47

Use the following duration times (seconds)of 24 eruptions of the Old Faithful geyser in
Yellowstone National Park. The duration times are sorted from lowest to highest. Describe how to calculate the limits to determine outliers for this data set? Identify any
outliers.

Question 48

A comparison is made between summer electric bills of those who have central air and those who have window units. Find the mean and median for each of the two samples,
then compare the two sets of results.

Question 49

Construct a data set for which the range is misleading as a measure of variation.
the range is misleading and suggest an alternative measure of variation.

Question 50

Describe any similarities or differences in the two distributions represented by the following
boxplots. Assume the two boxplots have the same scale.

Question 51

An engineer is designing a machine to manufacture gloves and she obtains the following
sample of hand lengths (mm)of randomly selected adult males based on data gathered: Define this data set as discrete or continuous. The hand lengths is what type of level of
measurement? Compare the mean and median for this data set and if you can draw any
conclusions from these values.

Question 52

Explain how two data sets could have equal means and modes but still differ greatly. Give
an example with two data sets to illustrate.

Question 53

The tallest living man has a height of 247 cm and the tallest living woman is 236 cm tall.
Heights of mean have a mean of 175 cm and a standard deviation of 7 cm. Heights of women
have a mean of 162 cm and a standard deviation of 6 cm. Relative to the population of the
same gender, determine who is taller by comparing z scores. Include an explanation.

Question 54

A male student of the author has a measured pulse rate of 52 beats per minute. According to a
National Center for Health Statistics data set, males have a mean pulse rate of 67.3 beats per
minute and a standard deviation of 10.3 beats per minute. Determine whether the student's
pulse rate is significantly low or high by determining the difference between the student's
pulse rate and the mean pulse rate of males and how many standard deviations that difference
represents by calculating the z score. Consider usual pulse rates to be within 2 standard
deviations of the mean.

Question 55

The table below provides a frequency distribution for the winner of the Davis Cup Tennis
Competition during the period 1977-1994.

Question 56

An engineer is designing a machine to manufacture gloves and she obtains the following
sample of hand lengths (mm)of randomly selected adult males. A frequency distribution is
created from the data. The frequencies in order are 1, 8, 56, 237, 382, 228, 48, 4, 1. Does it
appear that the sample is from a population with a normal distribution? Explain.

Question 57

If your score on your next statistics test is converted to a z score, which of these z scores would
you prefer? Explain your answer.

Question 58

Carbon monoxide is measured in one city for five different days. The mean of those values is
0.62 parts per million. Four of the values (in parts per million)are 0.3, 0.4, 1.1, and 0.7. Find
the missing value. If n is the number of values, how many of the n values can be freely
assigned before the remaining values are determined? What is that called?

Question 59

Use the following duration times (seconds)of 24 eruptions of the Old Faithful geyser in
Yellowstone National Park. The duration times are sorted from lowest to highest. Construct a boxplot and make observations about the shape, if there is skewness including in
what direction, and if there are any outliers. Explain the skewness in terms of the difference
between Q1 and the median and Q3 and the median.