# A+ Answers - Describe how data outliers

Describe how data outliers might be revealed in histograms and stem-and-leaf plots.

A. Any large values might indicate potential outliers.

B.Any large gaps between bars or stems might indicate potential outliers.

C. Large concentrations of data values might indicate potential outliers.

D. Any small values might indicate potential outliers.

In a grouped frequency distribution one interval is listed as 50-54. Assuming that the scores are measuring a continuous variable, what are the real limits of this interval?

50 and 54

50.5 and 54.5

49.5 and 54.5

50.5 and 53.5

For the following distribution, what is the highest score?

X f

20 - 25 2

15 - 19 5

10 - 14 4

5 - 9 1A. 5

B. 20

C. 25

D. cannot be determined

In general, what is the relationship between the standard deviation and variance?

A. Standard deviation equals the squared variance.

B. These two measures are unrelated.

C. Standard deviation is the square root of variance.

D. Variance is the square root of standard deviation.

Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement.

A. nominal

B. ordinal

C. interval

D. ratio

Determining a person's age (in years) would involve measurement on a(n) _____ scale of measurement.

A. nominal

B. ordinal

C. interval

D. ratio

A performance evaluation for new sales representatives at Office Automation Incorporated involves several ratings done on a scale of 1 to 10, with 10 the highest rating. The activities rated include new contacts, successful contacts, total contacts, dollar volume of sales, and reports. Then an overall rating is determined by using a weighted average. The weights are 1 for new contacts, 3 for successful contacts, 3 for total contacts, 5 for dollar value of sales, and 4 for reports. What would the overall rating be for a sales representative with ratings of 3 for new contacts, 5 for successful contacts, 9 for total contacts, 5 for dollar volume of sales, and 10 for reports? (Round your answer to two decimal places.)

Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L).

1.9 2 5.7 4.6 1.9 8.6 3.9 7.2

(a) Find the mean, median, and mode. (Round your answers to two decimal places.)

mean median mode (b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.)

range(c) Based on the data, would you recommend radon mitigation in this house? Explain.

A. Yes, since the average value is over "acceptable" ranges, although the median value is not.

B. Yes, since the median value is over "acceptable" ranges, although the mean value is not.

C. Yes, since the average and median values are both over "acceptable" ranges.

D. No, since the average and median values are both under "acceptable" ranges.

For the scores shown in the following stem and leaf display, how many people had scores in the 70s?

9 3 7 4

8 9 4 5

7 7 0 4 2

6 6 8

5 1 4

ANSWERS

A. 1

B. 2

C. 3

D. 4

If all n = 10 individuals in a sample have exactly the same score, what value will have the sample standard deviation?

A. 0

B. 10

C. cannot determine from the information given

D. The standard deviation will equal the score.

In a distribution with μ = 40 and σ = 2, a score of X = 46 would be considered an extreme value (far out in the tail).

True

False

A variable that consists of indivisible categories with no other scores existing between neighboring categories is called a(n) ______ variable.

independent

dependent

discrete

continuous

What kind of frequency distribution graph is appropriate for scores measured on an interval or ratio scale?

only a histogram

only a polygon

either a histogram or a polygon

only a bar graph

Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on random samples of size 30, 50, and 100 from the same population.

attached to the file is the histogram charts

(a) Using the midpoint labels of the three histograms, what would you say about the estimated range of the population data from smallest to largest?

Complete the table giving the range of the sample data in each of the histograms.

Smallest Value Largest Value

Histogram (i)

Histogram (ii)

Histogram (ii)

Based on the completed table, select the most reasonable estimate of the range of the population data.

9 to 14

9 to 15

9.5 to 14

10 to 15

11 to 13

Does the bulk of the data seem to be between 10 and 14 in all three histograms?

Since there are very few outside the range 10 to 14, we can say that the bulk of the data is not between 10 and 14.

Since there are many values outside the range 10 to 14, we can say that the bulk of the data is not between 10 and 14.

Since there are many values outside the range 10 to 14, we can say that the bulk of the data is between 10 and 14.

The number of cat toys under the cat owner's couch is an example of a discrete variable.

True

False

Answer the following questions on probability:A bag of marbles contains 7 blue marbles, 8 red marbles, 6 yellow marbles and 9 black marbles.A marble is chosen at random. Determinea) The probability that the marble is blue.b) The probability that the marble is either blue or yellow.c) The probably the marble is not red.

a) P(blue) = (Number of blue) / (Total number) = 7 / (7 + 8 + 6 + 9) = 7/30

b) P(blue or yellow) = (Number of blue or yellow) / (Total number) = (7 + 6) / 30 = 13/30

c) P(not red) = (Number not red) / (Total number) = (7 + 6 + 9) / 30 = 22/30 = 11/15

d) Let x be the number of broken eggs in a randomly selected carton of one dozen eggs at Second Hand Foods - a not so popular retailer. Determine the missing probability.x P(x)

0 ?

1 0.2

2 0.1

3 0.3

4 0.2

Provide explanations with your answers and use the f subscript x key to enter equations if necessary.

Let x be the random variable representing annual percent return for the Vanguard Total Stock Index (stocks only). Let y be a random variable representing annual return for a balanced index (60% stocks and 40% bonds). The standard deviations of x and y are 20.86 and 12.15, respectively. Answer the following questions related to this table:x 13 0 36 22 32 24 25 -13 -13 -22

y 7 -2 27 16 23 17 16 -2 -3 -7

a) Find the mean of the x values. b) Find the mean of the y values. c) Compute an 75% Chebyshev interval around the mean of the y values. d) Find the Coefficient of Variation for x. e) Find the Coefficient of Variation for y. f) Which of x or y seems to have the greater spread about the mean? Explain how you got your answers. Use the f subscript x key to enter equations, if necessary.

In an observational study the observations and or measurements are conducted in such a way as to change the response of the variable being measured.

True

False

When Dr. Lacey's computer crashed this summer she purchased a new Windows 10 machine. She noticed something different about Free Cell solitaire. Previously, on the old computer, even though it had been running Windows 10 prior to crash, her win rate for Free Cell had been about 70%. With the new computer, her win rate jumped to 100%. Consequently, she began recording her times from start to automatic completion (win.) Here are the times (in minutes - the first column of the data represents times) for games 162 to 171. To show your work use the icon above the question. If you have some difficulty with the icon then try another browser, or else, enter type out your answers in words explaining the formulas you used.4:17 162

2:08 163

2:54 164

13:05 165

5:21 166

35:43 167

8:01 168

5:06 169

1:43 170

2:45 171Find, a) the mean

b) the median

c) the mode, if it exists. If mode cannot be found state it cannot be found.

d) the midrange.

e) One of the times seems to be an outlier. Which one? Suppose that it was recorded incorrectly and that the correct time was 5.02 minutes. Recalculate the mean and recalculate the mode. What is the effect of the outlier on this set of data?*corrected version

The median is less affected by the presence of outliers than is the mean.

True

False

Professor Igor kept a list of the number of students visiting his office each week for two semesters (30 weeks.) The results were

15 23 17 13 3 9 7 6 8 11

16 32 27 4 20 3 28 5 6 11

20 12 8 10 25 10 8 15 11 9

Find a) What is the variable in his study? Is the variable discrete or continuous?

b) the sample standard deviation and the population standard deviation. Which one should the professor use?

Provide explanations with your answers and use the key to enter equations if necessary.

A single die is rolled. What is the probability that a number less than seven is obtained?

1 over 6

1

0

7 over 6

None of these

Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth.

24 17 15 33 25

A. 7.16

B. 9.58

C. 6.40

D. 8.57

E. 9.60

Find the area under the standard normal curve to the right of z = 1.

A.

0.5398

B.

0.8413

C.

0.1587

D.

0.1397

E.

None of these

Find the area under the standard normal curve over the interval specified below.

Between z = 1 and 2a.

0.819

b.

0.021

c.

0.341

d.

0.136

e.

0.976

Richard has been given an 11-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. What is the value of p? Round your answer to the nearest tenth.

A.

3.3

B.

3.7

C.

11.0

D.

33.0

E.

0.3

Give an example of a continuous random variable.

A.

The number of fish caught by a fishing boat

B.

The number of coins contained in a slot machine

C.

The number of tables sold at a furniture store

D.

The number of traffic accidents in a city

E.

The number of gallons of water in a reservoir

Approximately what percent of the area of the normal curve is betweenu -3dand3 + d

A.

99.7

B.

50

C.

68

D.

95

E.

None of these

The normal curve can be used to approximate the binomial proportion by making a continuity correction.

True

False

A quiz consists of 920 true or false questions. If a student guesses on each question, what is the mean number of correct answers?

A.

0

B.

920

C.

184

D.

460

E.

None of these

Give an example of a discrete random variable.

A.

The number of beverages sold at a lemonade stand

B.

The time required for a runner to finish a marathon

C.

The number of inches of rainfall in a county

D.

The temperature of a pot roast cooking in an oven

E.

The number of gallons of concrete used at a construction site

Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities (to the nearest thousandths.)

P(13 ≤ x ≤ 32); μ = 18; σ = 5a.

0.997b.

0.159c.

0.003d.

0.964e.

0.839

A larger sample size produces a longer confidence interval for the population mean.

True

False

Find the t-value such that the area left of the t-value is 0.025 with 17 degrees of freedom.

A.

-3.222

B.

2.110

C.

2.120

D.

-2.11

E.

None of these

Construct a 90% confidence interval for the population mean,. Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of 2.86 with a standard deviation of 0.78. Round to the nearest hundredth.

A.

(2.51,3.21)

B.

(2.28,3.66)

C.

(2.41,3.42)

D.

(2.37,3.56)

E.

None of these

To compute a confidence interval of the population mean when the population standard deviation is unknown we use the z distribution.

True

False

Professor Whata Guy surveyed a random sample of 420 statistics students. One of the questions was "Will you take another mathematics class?" The results showed that 252 of the students said yes. What is the sample proportion of the students who say they will take another math class?

A.

0.6

B.

0.775

C.

0.42

D.

0.252

E.

None of these

Suppose a population has a mean weight of 180 pounds and a standard deviation of 25 pounds. A sample of 100 items is drawn from this population. What is the standard error of the mean?

A.

2.5

B.

18.0

C.

1.8

D.

0.25

E.

None of these

Suppose that x has a distribution with μ = 14 and σ = 8. If a random sample is taken of size n = 53, find .

a.

1.10

b.

14.00

c.

30.29

d.

1.92

e.

8.00

Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of 6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 124.

A.

0.8615

B.

0.9938

C.

0.0062

D.

0.9998

E.

None of these

A. Any large values might indicate potential outliers.

B.Any large gaps between bars or stems might indicate potential outliers.

C. Large concentrations of data values might indicate potential outliers.

D. Any small values might indicate potential outliers.

In a grouped frequency distribution one interval is listed as 50-54. Assuming that the scores are measuring a continuous variable, what are the real limits of this interval?

50 and 54

50.5 and 54.5

49.5 and 54.5

50.5 and 53.5

For the following distribution, what is the highest score?

X f

20 - 25 2

15 - 19 5

10 - 14 4

5 - 9 1A. 5

B. 20

C. 25

D. cannot be determined

In general, what is the relationship between the standard deviation and variance?

A. Standard deviation equals the squared variance.

B. These two measures are unrelated.

C. Standard deviation is the square root of variance.

D. Variance is the square root of standard deviation.

Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement.

A. nominal

B. ordinal

C. interval

D. ratio

Determining a person's age (in years) would involve measurement on a(n) _____ scale of measurement.

A. nominal

B. ordinal

C. interval

D. ratio

A performance evaluation for new sales representatives at Office Automation Incorporated involves several ratings done on a scale of 1 to 10, with 10 the highest rating. The activities rated include new contacts, successful contacts, total contacts, dollar volume of sales, and reports. Then an overall rating is determined by using a weighted average. The weights are 1 for new contacts, 3 for successful contacts, 3 for total contacts, 5 for dollar value of sales, and 4 for reports. What would the overall rating be for a sales representative with ratings of 3 for new contacts, 5 for successful contacts, 9 for total contacts, 5 for dollar volume of sales, and 10 for reports? (Round your answer to two decimal places.)

Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L).

1.9 2 5.7 4.6 1.9 8.6 3.9 7.2

(a) Find the mean, median, and mode. (Round your answers to two decimal places.)

mean median mode (b) Find the sample standard deviation, coefficient of variation, and range. (Round your answers to two decimal places.)

range(c) Based on the data, would you recommend radon mitigation in this house? Explain.

A. Yes, since the average value is over "acceptable" ranges, although the median value is not.

B. Yes, since the median value is over "acceptable" ranges, although the mean value is not.

C. Yes, since the average and median values are both over "acceptable" ranges.

D. No, since the average and median values are both under "acceptable" ranges.

For the scores shown in the following stem and leaf display, how many people had scores in the 70s?

9 3 7 4

8 9 4 5

7 7 0 4 2

6 6 8

5 1 4

ANSWERS

A. 1

B. 2

C. 3

D. 4

If all n = 10 individuals in a sample have exactly the same score, what value will have the sample standard deviation?

A. 0

B. 10

C. cannot determine from the information given

D. The standard deviation will equal the score.

In a distribution with μ = 40 and σ = 2, a score of X = 46 would be considered an extreme value (far out in the tail).

True

False

A variable that consists of indivisible categories with no other scores existing between neighboring categories is called a(n) ______ variable.

independent

dependent

discrete

continuous

What kind of frequency distribution graph is appropriate for scores measured on an interval or ratio scale?

only a histogram

only a polygon

either a histogram or a polygon

only a bar graph

Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on random samples of size 30, 50, and 100 from the same population.

attached to the file is the histogram charts

(a) Using the midpoint labels of the three histograms, what would you say about the estimated range of the population data from smallest to largest?

Complete the table giving the range of the sample data in each of the histograms.

Smallest Value Largest Value

Histogram (i)

Histogram (ii)

Histogram (ii)

Based on the completed table, select the most reasonable estimate of the range of the population data.

9 to 14

9 to 15

9.5 to 14

10 to 15

11 to 13

Does the bulk of the data seem to be between 10 and 14 in all three histograms?

Since there are very few outside the range 10 to 14, we can say that the bulk of the data is not between 10 and 14.

Since there are many values outside the range 10 to 14, we can say that the bulk of the data is not between 10 and 14.

Since there are many values outside the range 10 to 14, we can say that the bulk of the data is between 10 and 14.

The number of cat toys under the cat owner's couch is an example of a discrete variable.

True

False

Answer the following questions on probability:A bag of marbles contains 7 blue marbles, 8 red marbles, 6 yellow marbles and 9 black marbles.A marble is chosen at random. Determinea) The probability that the marble is blue.b) The probability that the marble is either blue or yellow.c) The probably the marble is not red.

a) P(blue) = (Number of blue) / (Total number) = 7 / (7 + 8 + 6 + 9) = 7/30

b) P(blue or yellow) = (Number of blue or yellow) / (Total number) = (7 + 6) / 30 = 13/30

c) P(not red) = (Number not red) / (Total number) = (7 + 6 + 9) / 30 = 22/30 = 11/15

d) Let x be the number of broken eggs in a randomly selected carton of one dozen eggs at Second Hand Foods - a not so popular retailer. Determine the missing probability.x P(x)

0 ?

1 0.2

2 0.1

3 0.3

4 0.2

Provide explanations with your answers and use the f subscript x key to enter equations if necessary.

Let x be the random variable representing annual percent return for the Vanguard Total Stock Index (stocks only). Let y be a random variable representing annual return for a balanced index (60% stocks and 40% bonds). The standard deviations of x and y are 20.86 and 12.15, respectively. Answer the following questions related to this table:x 13 0 36 22 32 24 25 -13 -13 -22

y 7 -2 27 16 23 17 16 -2 -3 -7

a) Find the mean of the x values. b) Find the mean of the y values. c) Compute an 75% Chebyshev interval around the mean of the y values. d) Find the Coefficient of Variation for x. e) Find the Coefficient of Variation for y. f) Which of x or y seems to have the greater spread about the mean? Explain how you got your answers. Use the f subscript x key to enter equations, if necessary.

In an observational study the observations and or measurements are conducted in such a way as to change the response of the variable being measured.

True

False

When Dr. Lacey's computer crashed this summer she purchased a new Windows 10 machine. She noticed something different about Free Cell solitaire. Previously, on the old computer, even though it had been running Windows 10 prior to crash, her win rate for Free Cell had been about 70%. With the new computer, her win rate jumped to 100%. Consequently, she began recording her times from start to automatic completion (win.) Here are the times (in minutes - the first column of the data represents times) for games 162 to 171. To show your work use the icon above the question. If you have some difficulty with the icon then try another browser, or else, enter type out your answers in words explaining the formulas you used.4:17 162

2:08 163

2:54 164

13:05 165

5:21 166

35:43 167

8:01 168

5:06 169

1:43 170

2:45 171Find, a) the mean

b) the median

c) the mode, if it exists. If mode cannot be found state it cannot be found.

d) the midrange.

e) One of the times seems to be an outlier. Which one? Suppose that it was recorded incorrectly and that the correct time was 5.02 minutes. Recalculate the mean and recalculate the mode. What is the effect of the outlier on this set of data?*corrected version

The median is less affected by the presence of outliers than is the mean.

True

False

Professor Igor kept a list of the number of students visiting his office each week for two semesters (30 weeks.) The results were

15 23 17 13 3 9 7 6 8 11

16 32 27 4 20 3 28 5 6 11

20 12 8 10 25 10 8 15 11 9

Find a) What is the variable in his study? Is the variable discrete or continuous?

b) the sample standard deviation and the population standard deviation. Which one should the professor use?

Provide explanations with your answers and use the key to enter equations if necessary.

A single die is rolled. What is the probability that a number less than seven is obtained?

1 over 6

1

0

7 over 6

None of these

Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth.

24 17 15 33 25

A. 7.16

B. 9.58

C. 6.40

D. 8.57

E. 9.60

Find the area under the standard normal curve to the right of z = 1.

A.

0.5398

B.

0.8413

C.

0.1587

D.

0.1397

E.

None of these

Find the area under the standard normal curve over the interval specified below.

Between z = 1 and 2a.

0.819

b.

0.021

c.

0.341

d.

0.136

e.

0.976

Richard has been given an 11-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. What is the value of p? Round your answer to the nearest tenth.

A.

3.3

B.

3.7

C.

11.0

D.

33.0

E.

0.3

Give an example of a continuous random variable.

A.

The number of fish caught by a fishing boat

B.

The number of coins contained in a slot machine

C.

The number of tables sold at a furniture store

D.

The number of traffic accidents in a city

E.

The number of gallons of water in a reservoir

Approximately what percent of the area of the normal curve is betweenu -3dand3 + d

A.

99.7

B.

50

C.

68

D.

95

E.

None of these

The normal curve can be used to approximate the binomial proportion by making a continuity correction.

True

False

A quiz consists of 920 true or false questions. If a student guesses on each question, what is the mean number of correct answers?

A.

0

B.

920

C.

184

D.

460

E.

None of these

Give an example of a discrete random variable.

A.

The number of beverages sold at a lemonade stand

B.

The time required for a runner to finish a marathon

C.

The number of inches of rainfall in a county

D.

The temperature of a pot roast cooking in an oven

E.

The number of gallons of concrete used at a construction site

Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities (to the nearest thousandths.)

P(13 ≤ x ≤ 32); μ = 18; σ = 5a.

0.997b.

0.159c.

0.003d.

0.964e.

0.839

A larger sample size produces a longer confidence interval for the population mean.

True

False

Find the t-value such that the area left of the t-value is 0.025 with 17 degrees of freedom.

A.

-3.222

B.

2.110

C.

2.120

D.

-2.11

E.

None of these

Construct a 90% confidence interval for the population mean,. Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of 2.86 with a standard deviation of 0.78. Round to the nearest hundredth.

A.

(2.51,3.21)

B.

(2.28,3.66)

C.

(2.41,3.42)

D.

(2.37,3.56)

E.

None of these

To compute a confidence interval of the population mean when the population standard deviation is unknown we use the z distribution.

True

False

Professor Whata Guy surveyed a random sample of 420 statistics students. One of the questions was "Will you take another mathematics class?" The results showed that 252 of the students said yes. What is the sample proportion of the students who say they will take another math class?

A.

0.6

B.

0.775

C.

0.42

D.

0.252

E.

None of these

Suppose a population has a mean weight of 180 pounds and a standard deviation of 25 pounds. A sample of 100 items is drawn from this population. What is the standard error of the mean?

A.

2.5

B.

18.0

C.

1.8

D.

0.25

E.

None of these

Suppose that x has a distribution with μ = 14 and σ = 8. If a random sample is taken of size n = 53, find .

a.

1.10

b.

14.00

c.

30.29

d.

1.92

e.

8.00

Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of 6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 124.

A.

0.8615

B.

0.9938

C.

0.0062

D.

0.9998

E.

None of these

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