Deck 3: Describing, Exploring, and Comparing Data

Question 1

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

Answer 1

B

Question 2

Use the given sample data to find

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

Answer 2

61.0

Question 3

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

Answer 3

27 vehicles

Question 4

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.

Question 5

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 6

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 7

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

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

Question 8

Question 9

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 10

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 11

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 12

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.

Question 13

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

A)
B)
C)
D)

Question 14

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 15

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

Question 16

The test scores of 40 students are listed below.

Question 17

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

Question 18

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

A) 11.8
B ) 7 . 7
C ) 7 . 8
D) 6.2

Question 19

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 20

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 21

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 22

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 23

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.

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 24

Jorge has his own business as a painter. The amounts he made in the last five months are shown below:

Question 25

The local Tupperware dealers earned these commissions last month:

Question 26

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 27

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 28

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

Question 29

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 30

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 31

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 32

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 33

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 34

The test scores of 40 students are listed below. Find

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

Question 35

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.

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

Question 36

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 37

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 38

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 39

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 40

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 41

Which measure of center, the mean, the median, or the mode is most appropriate here? Why?
Dave is a college student contemplating a possible career option. One factor that will influence his decision is the amount of money he is likely to make. He decides to look up the
average salary of graduates in that profession. Which information would be more useful to
him, the mean salary or the median salary. Why?

Question 42

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 43

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 44

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 45

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 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.

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 and the median and and the median.

Question 48

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 49

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 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. 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 52

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.
-2.50, -1.50, 0, 1.00, 2.25

Question 53

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 54

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

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

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 57

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 58

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 59

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 60

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.