Statistics Review Questions

Table of Contents

Preface

This page contains review questions for teaching ITSE-1302 Computer Programming: Scientific Python 1 at Austin Community College in Austin, TX.

The questions and the answers on this page are connected by hyperlinks to make it easy for you to navigate from the question to the answer and back again.

The questions on this page are similar to the questions that you will find on the test for this competency. Therefore, it is strongly recommended that you study the material until you thoroughly understand the material covered by these questions.

Questions

Question 1.

True or False: Positive correlation is a relationship between two variables in which the dependent variable decreases as the independent variable increases.

Answer 1

Question 2

You create a scatter plot to show the relationship between two variables and draw a best fit line through the points. The line slopes upward going from left to right. This is an indication of which of the following:

A. A positive correlation.

B. A negative correlation.

C. Neither of the above.

Answer 2

Question 3

You create a scatter plot to show the relationship between two variables and draw a best fit line through the points. The line slopes upward going from left to right. This is an indication of which of the following:

A. A positive causation.

B. A negative causation.

C. Neither of the above.

Answer 3

Question 4

You create a relative frequency histogram of your data with five bins and the values in the bins going from left to right are the following:

0.05, 0.24, 0.4, 0.24, 0.05

This is most indicative of which of the following:

A. A left-skewed or negatively-skewed distribution.

B. A normal distribution.

C. A right-skewed or positively-skewed distribution.

D. None of the above.

Answer 4

Question 5

You create a relative frequency histogram of your data with five bins and the values in the bins going from left to right are the following:

0.05, 0.5, 0.4, 0.24, 0.05

This is most indicative of which of the following:

A. A left-skewed or negatively-skewed distribution.

B. A normal distribution.

C. A right-skewed or positively-skewed distribution.

D. None of the above.

Answer 5

Question 6

You create a relative frequency histogram of your data with five bins and the values in the bins going from left to right are the following:

0.05, 0.24, 0.4, 0.5, 0.05

This is most indicative of which of the following:

A. A left-skewed or negatively-skewed distribution.

B. A normal distribution.

C. A right-skewed or positively-skewed distribution.

D. None of the above.

Answer 6

Question 7

Which of the following are theoretically true for a normal distribution? Check all that apply.

A. The mean is greater than the median.

B. The mean and the median are greater than the mode.

C. The median is greater than the mean.

D. The mean and the median are less than the mode.

E. The mean, the median, and the mode are equal.

F. None of the above.

Answer 7

Question 8

Which of the following is true for a right-skewed or positively skewed distribution?.

A. The mean is typically greater than the median.

B. The median is typically greater than the mean.

C. The mean, the median, and the mode are equal.

D. None of the above.

Answer 8

Question 9

Which of the following is true for a left-skewed or negatively skewed distribution?

A. The mean is typically greater than the median.

B. The median is typically greater than the mean.

C. The mean, the median, and the mode are equal.

D. None of the above.

Answer 9

Question 10

Given a sample from a heavily skewed population, which of the following probably is most representative of the center of the population?

A. The mean of the sample.

B. The median of the sample.

C. Neither of the above.

Answer 10

Question 11

Which of the following most closely approximates the Interquartile Range (IQR) of a distribution?

A. 25%

B. 50%

C. 75%

D. None of the above.

Answer 11

Question 12

Which of the following are shown by a box and whisker plot? Check all that apply.

A. center

B. spread

C. range

D. standard deviation

E. variance

Answer 12

Question 13

Which if any of the following is a very close approximation of the percentage of a normal distribution that falls within plus and minus one standard deviation of the mean?

A. 25.5%

B. 50.5%

C. 75.5%

D. 100.5%

E. None of the above.

Answer 13

Question 14

Which if any of the following is a very close approximation of the percentage of a normal distribution that falls within plus and minus two standard deviations of the mean?

A. 17.5%

B. 34.5%

C. 68.5%

D. 95.5%

E. 110.5%

Answer 14

Question 15

True or False?  Subtracting the mean value from every value in a dataset will change the overall shape of the distribution.

Answer 15

Question 16

True or False? Subtracting the mean value from every value in a dataset and then multiplying every value by a constant will change the standard deviation of the distribution.

Answer 16

Question 17

True or False? Given a cubic die with six faces and and the numerals 1, 2, 3, 4, 5, and 6 printed on the faces, the probability that a 6 will appear in one roll of the die is 0.1667 or 16.67%.

Answer 17

Question 18

True or False? Given two cubic die, each with six faces and the numbers 1, 2, 3, 4, 5, and 6 printed on the faces, the probability that a 6 will appear on each die when you roll two die simultaneously is 5.54%.

Answer 18

Question 19

True or False? A histogram is a graphical display of data using bars of different heights. In a histogram, each bar groups numbers into ranges. Taller bars show that more data falls within that range. A histogram displays a visual estimate of the shape and spread of continuous sample data.

Answer 19

Question 20

True or False? The median of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The mean is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Answer 20


Answers

Answer 20

False.

Explanation

Mean and median were reversed in the statement. To be true, the statement would read:

The mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Back to Question 20

Answer 19

True.

Explanation

See https://www.khanacademy.org/math/probability/data-distributions-a1/displays-of-distributions/v/histograms-intro for example.

Back to Question 19

Answer 18

False. 

Explanation

The probability is one part in 36 or 2.78%.

Back to Question 18

Answer 17

True.

Explanation

The probability is one part in six or 16.67%.

Back to Question 17

Answer 16

True.

Explanation

This is a commonly-used way to change the standard deviation of a dataset.

Back to Question 16

Answer 15

False.

Explanation

Subtracting the mean value from every value in a dataset simply slides the distribution along the horizontal axis causing it to be centered at zero. It does not change the shape of the distribution.

Back to Question 15

Answer 14

D. 95.5%

Explanation

Approximately 95.45% of a normal distribution falls within plus and minus two standard deviations of the mean. See https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule for example.

Back to Question 14

Answer 13

E. None of the above.

Explanation

Approximately 68.27% of a normal distribution falls within plus and minus one standard deviation of the mean? See https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule for example.

Back to Question 13

Answer 12

A. center

B. spread

C. range

Explanation

The variance and the standard deviation are not shown by a box and whisker plot. The other items in the list are shown.

Back to Question 12

Answer 11

B. 50%

Explanation

The IQR contains two quarters or 50% of the data values.

Back to Question 11

Answer 10

B. The median of the sample.

Explanation

See http://condor.depaul.edu/sjost/it223/documents/central.htm for example.

Back to Question 10

Answer 9

B. The median is typically greater than the mean.

Explanation

See "Statistics Exercises Part 2".

Also see http://www.statisticshowto.com/probability-and-statistics/skewed-distribution/ for example.

Back to Question 9

Answer 8

A. The mean is typically greater than the median.

Explanation

See "Statistics Exercises Part 2".

Also see http://www.statisticshowto.com/probability-and-statistics/skewed-distribution/ for example.

Back to Question 8

Answer 7

E. The mean, the median, and the mode are equal.

Explanation

See "Statistics Exercises Part 2".

Theoretically, the mean, the median, and the mode are all equal for a dataset with a normal distribution.

Back to Question 7

Answer 6

A. A left-skewed or negatively-skewed distribution.

Explanation

See "Statistics Exercises Part 1".

Also see http://www.statisticshowto.com/probability-and-statistics/skewed-distribution/ for example.

Back to Question 6

Answer 5

C. A right-skewed or positively-skewed distribution.

Explanation

See "Statistics Exercises Part 1".

Also see http://www.statisticshowto.com/probability-and-statistics/skewed-distribution/ for example.

Back to Question 5

Answer 4

B. A normal distribution.

Explanation

See "Statistics Exercises Part 1".

Also see http://www.statisticshowto.com/probability-and-statistics/skewed-distribution/ for example.

Back to Question 4

Answer 3

C. Neither of the above.

Explanation

The plot indicates a positive correlation but correlation does not imply causation.

See "Statistics Exercises Part 1"

Back to Question 3

Answer 2

A. A positive correlation.

Explanation

See "Statistics Exercises Part 1"

Back to Question 2

Answer 1

False.

Explanation

That is the description of a negative correlation.

See "Statistics Exercises Part 1"

Also see https://study.com/academy/lesson/negative-correlation-in-psychology-examples-definition-interpretation.html/a> for example.

Back to Question 1

Housekeeping material

File name: StatisticsReview.htm

Revised: 04/24/18

Copyright 2018, Richard Baldwin

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