Deck 3: Descriptive Statistics

Question 1

A nonzero value of the skewness indicates asymmetry of the distribution of the data.

Answer 1

True

Question 2

If the mean of a distribution is greater than the median,then the distribution is positively skewed.

Answer 2

True

Question 3

An appropriate measure of central tendency for ordinal data is the mode.

Answer 3

False

Question 4

The median for ungrouped raw data is more complicated to compute then the median for grouped data.

Question 5

Computations of the variance and standard deviation using grouped data are potentially only approximation of the actual variance and standard deviation.

Question 6

The most frequently occurring value in a set of data is called the mode.

Question 7

The most appropriate measure of central tendency for nominal-level data is the median.

Question 8

Average deviation is a common measure of the variability of data containing a set of numbers.

Question 9

The sum of deviations about the arithmetic mean is always equal to zero.

Question 10

The average of the squared deviations about the arithmetic mean is called the variance.

Question 11

For grouped data,the midpoint of each class interval is used to represent all the values in a class interval.

Question 12

The coefficient of variation is unitless.

Question 13

Statistical measures used to yield information about the center or the middle parts of a group of numbers are called the measures of central tendency.

Question 14

Kurtosis is a measure of the association between two numerical variables.

Question 15

The sample standard deviation is calculated by taking the square root of the population standard deviation.

Question 16

For grouped data,the mode is the class midpoint of the modal class where the model class is the class interval with the greatest frequency.

Question 17

Skewness and kurtosis of a data set are measures of the shape of the distribution.

Question 18

The middle value in an ordered array of numbers is called the mode.

Question 19

The lowest appropriate level of measurement for the median is ordinal.

Question 20

It is inappropriate to use the mean to analyze data that are not at least interval level in measurement.

Question 21

A box and whisker plot is determined from the mean,the smallest and the largest values,and the lower and upper quartile.

Question 22

According to Chebyshev's Theorem how many values in a data set will be within 3 standard deviations of the mean?

A) At least 75%
B) At least 68%
C) At least 95%
D) At least 89%
E) At least 99%

Question 23

A sample was taken of the salaries of four employees from a large company.The following are their salaries (in thousands of dollars)for this year: 33,36,41,and 47.The variance of their salaries is approximately

A) 28.19
B) 75.59
C) 37.58
D) 6.13
E) 5.31

Question 24

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 34,39,41,35,and 41. The mean time (in minutes)required for this trip was _______.

A) 35
B) 41
C) 37.5
D) 38
E) 35.5

Question 25

The number of standard deviations that a value (x)is above or below the mean is the _________________.

A) absolute deviation
B) coefficient of variation
C) interquartile range
D) z score
E) correlation coefficient

Question 26

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the median grade?
B) 76
C) 82
D) 94
E) 95

Question 27

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 38,33,36,47,and 41. What is the variance for this sample data?

A) 28.5
B) 11
C) 22.8
D) 5.34
E) 4.77

Question 28

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the mode?

A) 79
B) 82
C) 86
D) 92
E) 76

Question 29

The empirical rule says that approximately what percentage of the values would be within 2 standard deviations of the mean in a bell shaped set of data?

A) 95%
B) 68%
C) 50%
D) 97.7%
E) 100%

Question 30

The empirical rule says that approximately what percentage of the values would be within 1 standard deviation of the mean in a bell shaped set of data?

A) 95%
B) 68%
C) 50%
D) 97.7%
E) 100%

Question 31

A sample was taken of the salaries of four employees from a large company.The following are their salaries (in thousands of dollars)for this year: 33,36,41,and 47.The median of their salaries is approximately

A) 38.5
B) 34.5
C) 34
D) 44.5
E) 38

Question 32

The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours.We can conclude that at least 75% of this brand of bulbs will last between _______.

A) 1100 and 1300 hours
B) 1150 and 1250 hours
C) 1050 and 1350 hours
D) 1000 and 1400 hours
E) 950 and 1450 hours

Question 33

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 34,39,41,35,and 41. The mode time required for this trip was _______.

A) 39
B) 41
C) 37.5
D) 38
E) 35

Question 34

An outlier of a data set is determined from the lower and upper quartile

Question 35

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 38,33,36,47,and 41. What is the standard deviation for this sample data?

A) 28.5
B) 11
C) 22.8
D) 5.34
E) 4.77

Question 36

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 44,39,41,35,and 41. What is the mean absolute deviation for this sample data?

A) 0
B) 12
C) 3
D) 2.4
E) 1.2

Question 37

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 34,39,41,35,and 41. The median time (in minutes)required for this trip was _______.

A) 39
B) 41
C) 37.5
D) 38
E) 35.5

Question 38

If the median of a distribution is greater than mean,then the distribution is skewed to the left.

Question 39

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the mean grade?

A) 78
B) 80
C) 86
D) 84
E) 88

Question 40

According to Chebyshev's Theorem,approximately how many values in a large data set will be within 2 standard deviations of the mean?

A) At least 75%
B) At least 68%
C) At least 95%
D) At least 89%
E) At least 99%

Question 41

An instructor is evaluating the performance of students on a test. He records the number of points that each student missed and created a frequency distribution. This is provided below: What is the standard deviation for this population?

A) 11.43
B) 14.14
C) 12.63
D) 13.17
E) 16.90

Question 42

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc.,suspects irregularities in the payroll system,and orders an inspection of "each and every payroll voucher issued since January 1,1993." Each payroll voucher was inspected and the following frequency distribution was compiled. The median number of errors per voucher is __________.

A) 3.67
B) 5
C) 3.25
D) 400
E) 3

Question 43

The following box and whisker plot was constructed for the age of accounts receivable. The box and whisker plot reveals that the accounts receivable ages are _______.

A) skewed to the left
B) skewed to the right
C) not skewed
D) normally distributed
E) symmetrical

Question 44

The ages of students in a class have been put into the frequency distribution below. What is the average age of these students?

A) 19.50
B) 19.83
C) 20.00
D) 22.00
E) 23.00

Question 45

An instructor is evaluating the performance of students on a test. He records the number of points that each student missed and created a frequency distribution. This is provided below: What is the mean number of points missed?

A) 20
B) 25
C) 29
D) 30
E) 35

Question 46

Liz Chapa manages a portfolio of 250 common stocks. Her staff compiled the following performance statistics for two new stocks. The coefficient of variation for Salas Products,Inc.is __________.

A) 300%
B) 100%
C) 33%
D) 5%
E) 23%

Question 47

The average starting salary for graduates at a university is $33,000 with a standard deviation of $2,000. If a histogram of the data shows that it takes on a mound shape,the empirical rule says that approximately 68% of the graduates would have a starting salary between _______.

A) 29,000 and 37,000
B) 27,000 and 39,000
C) 25,000 and 41,000
D) 29,000 and 37,000
E) 21,000 and 29,000

Question 48

Jessica Salas,president of Salas Products,is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1)an average life of 75 months,(2)a standard deviation of 5 months,and (3)a bell shaped battery life distribution.Approximately 99.7% of the batteries will last between ________________.

A) 70 and 80 months
B) 60 and 90 months
C) 65 and 85 months
D) 55 and 95 months
E) 50 and 100 months

Question 49

The following box and whisker plot was constructed for the age of accounts receivable. The box and whisker plot reveals that the accounts receivable ages are _______.

A) skewed to the left
B) skewed to the right
C) not skewed
D) normally distributed
E) symmetrical

Question 50

The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours. It can be concluded that at least 89% of this brand of bulbs will last between _______.

A) 1100 and 1300 hours
B) 1150 and 1250 hours
C) 1050 and 1350 hours
D) 1000 and 1400 hours
E) 950 and 1450 hours

Question 51

The average starting salary for graduates at a university is $33,000 with a standard deviation of $2,000. If a histogram of the data shows that it takes on a mound shape,the empirical rule says that approximately 95% of the graduates would have a starting salary between _______.

A) 29,000 and 37,000
B) 27,000 and 39,000
C) 25,000 and 41,000
D) 29,000 and 37,000
E) 21,000 and 29,000

Question 52

Jessica Salas,president of Salas Products,is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1)an average life of 75 months,(2)a standard deviation of 5 months,and (3)a bell shaped battery life distribution.Approximately 68% of the batteries will last between ________________.

A) 70 and 80 months
B) 60 and 90 months
C) 65 and 85 months
D) 55 and 95 months
E) 60 and 100 months

Question 53

The ages of students in a class have been put into the frequency distribution below. What is the standard deviation for this (population)set of data?

A) 0.494
B) 0.703
C) 1.12
D) 1.25
E) 1.35

Question 54

The ages of students in a class have been put into the frequency distribution below. What is the median age of these students?

A) 18
B) 19
C) 19.5
D) 20
E) 20.5

Question 55

Pinky Bauer,Chief Financial Officer of Harrison Haulers,Inc.,suspects irregularities in the payroll system,and orders an inspection of "each and every payroll voucher issued since January 1,1993." Each payroll voucher was inspected and the following frequency distribution was compiled. The mean number of errors per voucher is __________.

A) 3.67
B) 5
C) 750
D) 300
E) 8.7

Question 56

An instructor is evaluating the performance of students on a test. He records the number of points that each student missed and created a frequency distribution. This is provided below: What is the variance for this population?

A) 11.43
B) 135.17
C) 130.67
D) 180.67
E) 198.07

Question 57

The ages of students in a class have been put into the frequency distribution below. What is the mode age of these students?

A) 18
B) 19
C) 20
D) 21
E) 23

Question 58

Jessica Salas,president of Salas Products,is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1)an average life of 75 months,(2)a standard deviation of 5 months,and (3)a bell shaped battery life distribution.Approximately 95% of the batteries will last between ________________.

A) 70 and 80 months
B) 60 and 90 months
C) 65 and 85 months
D) 55 and 95 months
E) 60 and 100 months

Question 59

The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 75 hours. Tests show that the life of the bulb is approximately normally distributed. It can be concluded that approximately 68% of the bulbs will last between _______.

A) 900 and 1100 hours
B) 950 and 1050 hours
C) 975 and 1475 hours
D) 1050 and 1350 hours
E) 1125 and 1275 hours

Question 60

Jessica Salas,president of Salas Products,is reviewing the warranty policy for her company's new model of automobile batteries. Life tests performed on a sample of 100 batteries indicated: (1)an average life of 75 months,(2)a standard deviation of 5 months,and (3)a bell shaped battery life distribution.What percentage of the batteries will fail within the first 65 months of use?

A) 0.5%
B) 1%
C) 2.5%
D) 5%
E) 7.5%

Question 61

A statistics student made the following grades on the first 6 tests: 76,82,92,95,92,86.The total number of tests for the semester is 7.If the median score for the whole semester was 92,what could not have been the score of the last test?

A) 77
B) 92
C) 93
D) 94
E) 96

Question 62

Shaun Connor,Human Resources Manager forAmerican Oil Terminals (AOT),is reviewing the operator training hours at AOT nationally. His staff compiled the following table of national statistics on operators training hours. What can Shaun conclude from these statistics?

A) The East Coast distribution is skewed to the left.
B) The East Coast distribution is skewed to the right.
C) The West Coast distribution is skewed to the left.
D) The West Coast distribution is skewed to the right.
E) Both distributions are symmetrical.

Question 63

The ages of the machines in one of the production lines in your company are exhibited in the frequency distribution table below. Two additional machines have been added to the production line,and the median age of the machines didn't change.
What is the minimum number of new (0-year-old)machines that you need to purchase to change the median age of the machines?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 64

David Desreumaux,VP of Human Resources of American First Banks (AFB),is reviewing the employee training programs of AFB banks. His staff reports several statistics for teller training hours. The mean is 20 hours,the standard deviation is 5 hours,the median is 15 hours,and mode is 10 hours.The Pearsonian coefficient of skewness-or Pearson's second skewness coefficient,defined as (3 × (μ - median)/σ)-for teller training hours is __________.

A) 6
B) 1
C) 3
D) 4
E) 0

Question 65

An electrical component for one of the main products your company produces is specified to have an electrical impedance of 2.15 ohms.However,the manufacturing process is not perfect and there is some variation on the actual impedance of these components.A recent statistical study indicated that in fact,the impedances are normally distributed with a mean impedance of 2.15 ohms and a standard deviation of 0.05 ohms.When the impedance exceeds 2.25 ohms,the product malfunctions so that component must be rejected and replaced by one whose impedance is within the acceptable limit.If you need 1350 usable components,how many components should you order?

A) 1608
B) 1422
C) 1421
D) 1385
E) 1384

Question 66

A sample of 117 records of the selling price in dollars of homes from Feb 15 to Apr 30,2013 was taken from the files maintained by the Albuquerque Board of Realtors.The following are summary statistics for the selling prices. From this we can conclude that,

A) There are no outliers
B) More homes were sold for greater than $121750 than for less than $77650
C) 68% of the selling price of homes is from $77650 to $121750
D) 25% of the selling price of homes is at least $121750
E) The distribution of selling price of homes is negatively skewed.

Question 67

Karen Merlott,VP for Strategic Planning at a recruitment firm,recently conducts a survey to determine customer satisfaction with job placement.She distributed the survey to 45 of the most recently placed executives. Two items on a survey questionnaire them to rate the importance of "initial interview process" and "satisfaction of final job placement" on a scale of 1 to 10 (with 1 meaning "not important" and 10 meaning "highly important"). Her staff assembled the following statistics on these two items. What can Karen conclude from these statistics?

A) The Initial Interview Process distribution is positively skewed.
B) The Initial Interview Process distribution is not skewed.
C) The Satisfaction of Final Job Placement distribution is negatively skewed.
D) The Satisfaction of Final Job Placement distribution is positively skewed.
E) Both are symmetrically distributed.

Question 68

Your company is testing a new auto engine in a race car.The race car is going in a 2-mile track.If the first lap was exactly at 2 minutes,so that the average speed for the first lap was 1.00 mile per minute,what would be the time required for the second lap so that the overall average speed will be 2 miles per minute?

A) It's not possible to end up with an overall average speed of 4 miles per minute.
B) 1.0 minute
C) 0.8 minutes
D) 0.6 minutes
E) 0.4 minutes

Question 69

The following frequency distribution was constructed for the wait times to check out at the grocery store. The frequency distribution reveals that the wait times to check out at the grocery store are _______.

A) skewed to the left
B) skewed to the right
C) not skewed
D) normally distributed
E) symmetrical

Question 70

The mean life of a specialized essential electronic component in one of your company's main products is 80 months,and its standard deviation is 6 months.It is known that the life for this component is not normally distributed.We can conclude that at least 96% of these components will last between _______.

A) 74 and 86 months
B) 68 and 92 months
C) 66 and 94 months
D) 64 and 96 months
E) 50 and 110 months

Question 71

David Desreumaux,VP of Human Resources of American First Banks (AFB),is reviewing the employee training programs of AFB banks. His staff compiled the following table of regional statistics on teller training hours. What can David conclude from these statistics?

A) The Southeast distribution is symmetrical.
B) The Southwest distribution is skewed to the left.
C) The Southeast distribution has the greater dispersion.
D) The Southeast distribution is skewed to the left.
E) The two distributions are symmetrical.

Question 72

A statistics student has a mean score of 92 in the first 3 tests.Suppose there are a total of 4 tests and all of them have equal weight.You can also assume that there is no extra credit in the last test.What is the best possible final average this student can get?

A) 96
B) 95
C) 94
D) 93
E) there is not enough information to find out

Question 73

The frequency distribution table below shows the number of machines that produced a given number of defective products during the last semester.What is the median number of defective products?

A) 4
B) 4.25
C) 4.33
D) 4.5
E) 4.67

Question 74

A statistics student made the following grades on the first 6 tests: 76,82,92,95,79,86.The total number of tests for the semester is 7.What could be her median score for the whole semester?

A) It's not possible to answer without knowing the score on the last test.
B) 76
C) 82
D) 92
E) 95

Question 75

The following frequency distribution was constructed for the wait times in the emergency room. The frequency distribution reveals that the wait times in the emergency room are _______.

A) skewed to the left
B) skewed to the right
C) not skewed
D) normally distributed
E) symmetrical

Question 76

The ages of the machines in one of the production lines in your company are exhibited in the frequency distribution table below. What is the minimum number of 6-year-old machines that you need to retire to change the median age of the machines?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 77

The ages of the machines in one of the production lines in your company are exhibited in the frequency distribution table below. What is the median age of these machines?

A) 2
B) 3
C) 3.5
D) 4
E) 4.5

Question 78

You have computed the z score for a value.Then you realize that the actual standard deviation of the population is 25% larger than the one you used for computing the z value.Your corrected z value will be _______.

A) 25% smaller than the original value
B) 25% larger than the original value
C) 75% smaller than the original value
D) 20% larger than the original value
E) 20% smaller than the original value

Question 79

The mean life of a particular brand of light bulb is 1200 hours.If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours,then what is the standard deviation of the light bulbs' life?

A) 25
B) 50
C) 75
D) 100
E) 200

Question 80

In its Industry Norms and Key Business Ratios,Dun & Bradstreet reported that Q₁,Q₂,and Q₃ for 2,037 gasoline service stations' sales to inventory ratios were 20.8,33.4,and 53.8,respectively. From this we can conclude that ____________.

A) 68% of these service stations had sales to inventory ratios of 20.8 or less
B) 50% of these service stations had sales to inventory ratios of 33.4 or less
C) 50% of these service stations had sales to inventory ratios of 53.8 or more
D) 95% of these service stations had sales to inventory ratios of 33.4 or more
E) 99% of these service stations had sales to inventory ratios of 53.8 or more