1. COURSE: JUST 3900 INTRODUCTORY STATISTICS FOR CRIMINAL JUSTICE Test Review: Ch. 1-3 Peer Tutor Slides Instructor: Mr. Ethan W. Cooper, Lead Tutor © 2013 - - PLEASE DO NOT CITE, QUOTE, OR REPRODUCE WITHOUT THE WRITTEN PERMISSION OF THE AUTHOR. FOR PERMISSION OR QUESTIONS, PLEASE EMAIL MR. COOPER AT THE FOLLWING: coopere07@students.ecu.edu

2. Chapter 1: Intro to Stats Question 1: A psychology professor is interested in the tweeting habits of college freshman at ECU. If the professor measures the number of tweets that each freshman in her classes sends each day and calculates the average number for all of her classes, the average number would be an example of a ________. Question 1: A psychology professor is interested in the tweeting habits of college freshman at ECU. If the professor measures the number of tweets that each freshman in her classes sends each day and calculates the average number for all of her classes, the average number would be an example of a ________.

3. Chapter 1: Intro to Stats Question 1 Answer: Question 1 Answer: The average would be an example of a statistic because the professor conducted her research using a sample (the freshman in her classes, not the entire freshman class at ECU). The average would be an example of a statistic because the professor conducted her research using a sample (the freshman in her classes, not the entire freshman class at ECU).

4. Chapter 1: Intro to Stats Question 2: A researcher wants to know the relationship between gender and cell phone preference. He uses surveys asking men and women which they prefer: texting or calling. Is this an example of an experiment? Why or why not? Question 2: A researcher wants to know the relationship between gender and cell phone preference. He uses surveys asking men and women which they prefer: texting or calling. Is this an example of an experiment? Why or why not?

5. Chapter 1: Intro to Stats Question 2 Answer: Question 2 Answer: This would not be an example of an experiment because the researcher did not manipulate any variables; he simply observed the difference between the cell phone usage of men and women. This study would be correlational or nonexperimental. This would not be an example of an experiment because the researcher did not manipulate any variables; he simply observed the difference between the cell phone usage of men and women. This study would be correlational or nonexperimental.

6. Chapter 1: Intro to Stats Question 3: Suppose a researcher wanted to know the relationship between cell phone preference (texting or calling) and type of phone (flip phone or smart phone). To accomplish this he designs an experiment in which there are 2 groups. One group is issued iphones, while the other is issued flip phones. The researcher then records every call and text for a month to determine whether the type of phone influences cell phone preference. Identify the independent and dependent variables for this study. Question 3: Suppose a researcher wanted to know the relationship between cell phone preference (texting or calling) and type of phone (flip phone or smart phone). To accomplish this he designs an experiment in which there are 2 groups. One group is issued iphones, while the other is issued flip phones. The researcher then records every call and text for a month to determine whether the type of phone influences cell phone preference. Identify the independent and dependent variables for this study.

7. Chapter 1: Intro to Stats Question 3 Answer: Question 3 Answer: The independent variable is the type of phone. This is the variable that the researcher is manipulating; it affects the outcome of the dependent variable. The independent variable is the type of phone. This is the variable that the researcher is manipulating; it affects the outcome of the dependent variable. The dependent variable is cell phone preference. We expect the independent variable (type of phone) to have an effect on the dependent variable (cell phone preference). The dependent variable is cell phone preference. We expect the independent variable (type of phone) to have an effect on the dependent variable (cell phone preference).

8. Chapter 1: Intro to Stats Question 4: A survey asks students to identify their gender, age, and GPA. For each of these three variables, identify the scale of measurement that probably is used and identify whether the variable is discrete of continuous. Question 4: A survey asks students to identify their gender, age, and GPA. For each of these three variables, identify the scale of measurement that probably is used and identify whether the variable is discrete of continuous.

9. Chapter 1: Intro to Stats Question 4 Answer: Question 4 Answer: Gender is measured on a nominal scale and is discrete. Age and GPA are measured on ratio scales and are both continuous variables. Gender is measured on a nominal scale and is discrete. Age and GPA are measured on ratio scales and are both continuous variables.

10. Chapter 1: Intro to Stats Question 5: When measuring weight to the nearest half pounds, what are the real limits for a score of 150 lbs? Question 5: When measuring weight to the nearest half pounds, what are the real limits for a score of 150 lbs? Hint: The question wording here is slightly different than the way real limits are discussed in class, but the approach to calculating real limits is the same. In class, weight was discussed as being measured in whole pounds and real limits are calculated based upon half intervals above and below any given point in the weight scale. Thus, the real limits for a score of 150 pounds measured in whole pounds would be 145.5 to 150.5 (this is how you did this in class). Question #5 as written above in this slide indicates that weight was measured to the nearest half pound. This changes the calculation of real limits. Try to answer this yourself and then review the answer on the next slide to see if you answered this correctly.

11. Chapter 1: Intro to Stats Question 5 Answer: Question 5 Answer: URL 150.25 URL 150.25 LRL 149.75 LRL 149.75 149.5 150 150.5 149.75 150.25

12. Chapter 1: Intro to Stats

13. Exponents before summation.

14. Chapter 1: Intro to Stats Question 7: Use summation notation to express the following: Subtract 10 points from each score, square them and then add the resulting values. Question 7: Use summation notation to express the following: Subtract 10 points from each score, square them and then add the resulting values.

15. Chapter 1: Intro to Stats

16. Chapter 2: Frequency Distributions Question 1: Make a stem and leaf plot using the following set of N = 20 scores: Question 1: Make a stem and leaf plot using the following set of N = 20 scores: 14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18, 14, 11 14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18, 14, 11

17. Chapter 2: Frequency Distributions Question 1 Answer: Question 1 Answer: 14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18, 14, 11 14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18, 14, 11 StemLeaf 08996 146036205741841 272

18. Chapter 2: Frequency Distributions Question 2: If you were asked to create a grouped frequency table using the following set of N = 25 scores, how many intervals would you have and what would their width be? Question 2: If you were asked to create a grouped frequency table using the following set of N = 25 scores, how many intervals would you have and what would their width be? 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 78, 60 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 78, 60

19. Chapter 2: Frequency Distributions Question 2 Answer: Question 2 Answer: We want 9 intervals with a width of 5. We want 9 intervals with a width of 5. Remember the guidelines on pp. 42 and 43. For a grouped frequency distribution, we want about 10 intervals. Also, we want our interval width to be a simple number. Remember the guidelines on pp. 42 and 43. For a grouped frequency distribution, we want about 10 intervals. Also, we want our interval width to be a simple number. A width of 2 gives us 21 rows (too many) A width of 2 gives us 21 rows (too many) A width of 5 gives us 9 rows (OK) A width of 5 gives us 9 rows (OK) A width of 10 gives us 5 rows (too few) A width of 10 gives us 5 rows (too few)

20. Chapter 2: Frequency Distributions Question 3: What are the differences between histograms and a bar graphs? Question 3: What are the differences between histograms and a bar graphs?

21. Chapter 2: Frequency Distributions Question 3 Answer: Question 3 Answer: Histograms are used for interval and ratio data, while bar graphs are used for nominal or ordinal data. Histograms are used for interval and ratio data, while bar graphs are used for nominal or ordinal data. Bar graphs have space between the bars because they represent discrete variables. Bar graphs have space between the bars because they represent discrete variables. Histograms have no space between the bars because they represent continuous variables. Histograms have no space between the bars because they represent continuous variables.

22. Chapter 2: Frequency Distributions Question 4: Label each frequency distribution as symmetrical, positively skewed or negatively skewed. Question 4: Label each frequency distribution as symmetrical, positively skewed or negatively skewed.

23. Chapter 2: Frequency Distributions Question 4 Answer: Question 4 Answer: Positively SkewedNegatively Skewed Symmetrical

24. Chapter 2: Frequency Distributions Question 5: Find the 80 th percentile. Question 5: Find the 80 th percentile.

25. Chapter 2: Frequency Distributions Question 5 Answer: Question 5 Answer: Step 1: Find the width of the interval on both scales Step 1: Find the width of the interval on both scales 5 and 25 points, respectively 5 and 25 points, respectively Step 2: Locate position of intermediate value Step 2: Locate position of intermediate value 80% is located 15 points from top (15/25 = 3/5 of interval) 80% is located 15 points from top (15/25 = 3/5 of interval) Step 3: Use same fraction to determine corresponding position on other scale. First, determine the distance from the top of the interval Step 3: Use same fraction to determine corresponding position on other scale. First, determine the distance from the top of the interval Distance = Fraction x Width = (3/5) * (5 points) = 3 Points Distance = Fraction x Width = (3/5) * (5 points) = 3 Points Step 4: Use distance from top to determine the position on the other scale Step 4: Use distance from top to determine the position on the other scale 19.5 – 3 = 16.5 19.5 – 3 = 16.5 Thus, the 80 th percentile for X is 16.5. Thus, the 80 th percentile for X is 16.5.

26. Chapter 3: Central Tendency

29. Question 2 Answer: Question 2 Answer: The new score must be greater than 50. The new score must be greater than 50.

30. Chapter 3: Central Tendency

33. Question 4 Answer: Question 4 Answer: a) The new mean would be 55. b) The new mean would be 250.

34. Chapter 3: Central Tendency Question 5: Find the median for the distribution of scores: Question 5: Find the median for the distribution of scores: 1, 2, 2, 3, 4, 4, 4, 4, 4, 5 1, 2, 2, 3, 4, 4, 4, 4, 4, 5

35. Chapter 3: Central Tendency Question 5 Answer: Question 5 Answer: 1, 2, 2, 3, 4, 4, 4, 4, 4, 5 1, 2, 2, 3, 4, 4, 4, 4, 4, 5 Median: 4 Median: 4

36. Chapter 3: Central Tendency Question 6: The following is a distribution of measurements for a continuous variable. Find the precise median that divides the distribution exactly in half. Question 6: The following is a distribution of measurements for a continuous variable. Find the precise median that divides the distribution exactly in half. 1, 2, 2, 3, 4, 4, 4, 4, 4, 5 1, 2, 2, 3, 4, 4, 4, 4, 4, 5

37. Chapter 3: Central Tendency Question 6 Answer: Question 6 Answer: 1, 2, 2, 3, 4, 4, 4, 4, 4, 5 1, 2, 2, 3, 4, 4, 4, 4, 4, 5 Median: 3.70 (one-fifth of the way into the interval from 3.5 to 4.5). Median: 3.70 (one-fifth of the way into the interval from 3.5 to 4.5). 12 3 41 12 345 1/5 4/5

38. Chapter 3: Central Tendency Question 7: What is the mode of the following distribution? Question 7: What is the mode of the following distribution?

39. Chapter 3: Central Tendency

40. Question 8: Which measure of central tendency is most affected if one extremely large score is added to a distribution (mean, median, mode)? Question 8: Which measure of central tendency is most affected if one extremely large score is added to a distribution (mean, median, mode)?

41. Chapter 3: Central Tendency Question 8 Answer: Question 8 Answer: Mean. Mean. Notice that the mean follows the extreme scores.

42. Chapter 3: Central Tendency Question 9: Why is it usually considered inappropriate to compute a mean for scores measured on an ordinal scale? Question 9: Why is it usually considered inappropriate to compute a mean for scores measured on an ordinal scale?

43. Chapter 3: Central Tendency Question 9 Answer: Question 9 Answer: The definition of the mean is based on distances and ordinal scales do not measure distance. The definition of the mean is based on distances and ordinal scales do not measure distance.

44. Chapter 3: Central Tendency Question 10: In a perfectly symmetrical distribution, the mean, the median, and the mode will all have the same value. (True or False?) Question 10: In a perfectly symmetrical distribution, the mean, the median, and the mode will all have the same value. (True or False?)

45. Chapter 3: Central Tendency Question 10 Answer: Question 10 Answer: False, if the distribution is bimodal. False, if the distribution is bimodal.

46. Chapter 3: Central Tendency Question 11: A distribution with a mean of 70 and a median of 75 is probably positively skewed. (True or False?) Question 11: A distribution with a mean of 70 and a median of 75 is probably positively skewed. (True or False?)

47. Chapter 3: Central Tendency Question 11 Answer: Question 11 Answer: False. The mean is displaced toward the tail on the left-hand side. False. The mean is displaced toward the tail on the left-hand side. 70 75