Research Methods and Statistics A Critical Thinking Approach, 4th Edition by Sherri L. Jackson – Test Bank

Complete Test Bank With Answers

 

 

Sample Questions Posted Below

 

Chapter 5

Data Organization and Descriptive Statistics

Chapter Outline

Organizing Data

Frequency Distributions

Graphs

Bar Graphs and Histograms

Frequency Polygons

Descriptive Statistics

Measures of Central Tendency

Mean

Median

Mode

Measures of Variation

Range

Average Deviation and Standard Deviation

Types of Distributions

Normal Distributions

Kurtosis

Positively Skewed Distributions

Negatively Skewed Distributions

z-scores

z-scores, the Standard Normal Distribution, Probability, and Percentile Ranks

Summary

Review of Key Terms

Average Deviation—An alternative measure of variation that, like the standard deviation, indicates

the average difference between the scores in a distribution and the mean of the distribution.

Bar Graph—A graphical representation of a frequency distribution in which vertical bars are centered

above each category along the x-axis and are separated from each other by a space indicating that

the levels of the variable represent unrelated and distinct categories.

Class Interval Frequency Distribution—A table in which the scores are grouped into intervals and

listed along with the frequency of scores in each interval.

Descriptive Statistics—Numerical measures that describe a distribution by providing information on

the central tendency of the distribution, the width of the distribution, and the shape of the

distribution.

Frequency Distribution—A table in which all of the scores are listed along with the frequency with

which each occurs.

Frequency Polygon— A line graph of the frequencies of individual scores.

Histogram— A graphical representation of a frequency distribution in which vertical bars centered

above scores on the x-axis touch each other to indicate that the scores on the variable represent

related, increasing values.

55Kurtosis—How flat or peaked a normal distribution is.

Leptokurtic—Normal curves that are tall and thin with only a few scores in the middle of the

distribution having a high frequency.

Mean—A measure of central tendency; the arithmetic average of a distribution.

Measure of Central Tendency—A number intended to characterize an entire distribution.

Measure of Variation— A number that indicates how dispersed scores are around the mean of the

distribution.

Median—A measure of central tendency; the middle score in a distribution after the scores have been

arranged from highest to lowest or lowest to highest.

Mesokurtic—Normal curves that have peaks of medium height and distributions that are moderate in

breadth.

Mode—A measure of central tendency; the score in a distribution that occurs with the greatest

frequency.

Negatively Skewed Distribution—A distribution in which the peak is to the right of the center point

and the tail extends toward the left, or in the negative direction.

Normal Curve—A symmetrical, bell-shaped frequency polygon representing a normal distribution.

Normal Distribution—A theoretical frequency distribution having certain special characteristics.

Percentile Rank—A score that indicates the percentage of people who scored at or below a given raw

score.

Platykurtic—Normal curves that are short and more dispersed (broader).

Positively Skewed Distribution— A distribution in which the peak is to the left of the center point

and the tail extends toward the right, or in the positive direction.

Probability—The expected relative frequency of a particular outcome.

Qualitative Variable—A categorical variable for which each value represents a discrete category.

Quantitative Variable—A variable for which the scores represent a change in quantity.

Range—A measure of variation; the difference between the lowest and the highest score in a

distribution.

Standard Deviation—A measure of variation; the average difference between the scores in the

distribution and the mean or central point of the distribution, or more precisely, the square root of

the average squared deviation from the mean.

Standard Normal Distribution—A normal distribution with a mean of 0 and a standard deviation of

1.

Variance—The deviation squared.

56z-score (Standard Score)—A number that indicates how many standard deviation units a raw score is

from the mean of a distribution.

Relevant Articles from Handbook for Teaching Statistics and Research Methods (1st ed.)

Beins, B. Teching the relevance of statistics through consumer-oriented research. Pp. 5-6.

Dillbeck, M. C. Teaching statistics in terms of the knower. Pp. 20-23.

Dillon, K. M. Statisticophobia. P. 3.

Forsyth, G. A. A task-first individual-differences approach to designing a statistics and methodology

course. Pp. 15-17.

Hastings, M. W. Statistics: Challenge for students and the professor. Pp. 6-7.

Jacobs, K. W. Instructional techniques in the introductory statistics course: The first class meeting. P.

4.

Magnello, M. E., & Spies, C. J. Using organizing concepts to facilitate the teaching of statistics. Pp.

12-15.

Shatz, M. A. The Greyhound strike: Using a labor dispute to teach descriptive statistics. P. 35.

Ward, E. F. Statistics mastery: A novel approach. Pp. 17-20.

Relevant Articles from Handbook for Teaching Statistics and Research Methods (2nd ed.)

Beins, B. A BASIC program for generating integer means and variances. Pp. 9-10.

Pittenger, D. J. Teaching students about graphs. Pp. 16-20.

Web Resources

For step-by-step practice and information, have your students check out the Statistics and Research

Methods Workshops at www.cengage.com/psychology/workshops. In addition, practice quizzes,

vocabulary flashcards, and more are available at www.cengage.com/psychology/jackson.

Answers to Chapter Exercises

1. Speed f rf

62 1 .05

64 3 .15

65 4 .20

67 3 .15

68 2 .10

70 2 .10

72 1 .05

73 1 .05

76 1 .05

5779 1 .05

80 1 .05

20 1.00

2. Interval f rf

61-62 1 .05

63-64 3 .15

65-66 4 .20

67-68 5 .25

69-70 2 .10

71-72 1 .05

73-74 1 .05

75-76 1 .05

77-78 0 .00

79 -80 2 .10

20 1.00

3. Either a histogram or a frequency polygon could be used to graph these data. However, due to the

continuous nature of the speed data, a frequency polygon might be most appropriate. Both a

histogram and a frequency polygon of the data are presented.

Frequ ency

5

4

3

2

1

0

62

64

66

68

70

72

74

76

78

80

63

65

67

69

71

73

75

77

79

Speed (MPH)

Fre q u e n c y

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

.5

62.

64

65

67

68

70

72

Speed (MPH)

73

76

79

80

584. = 68.55

Md = 67

Mo = 65

The distribution is positively skewed.

5. a. = 7.3

Md = 8.5

Mo = 11

b. = 4.83

Md = 5

Mo = 5

c. = 6.17

Md = 6.5

Mo = 3, 8

d. = 5.5

Md = 6

Mo = 6

6. a. range = 8

s = 2.74

 = 2.58

AD = 2.22

b. range = 8

s = 2.74

 = 2.58

AD = 2.22

c. range = 80

s = 27.4

 = 25.8

AD = 22.2

d. range = .80

s = .274

 = .258

AD = .222

e. range = 800

s = 273.86

 = 258.20

AD = 222.22

7. a. z = +2.57

b. z = -2.0

c. z = +2.0

Proportion of cars that cost an equal amount or more = .0051

Proportion of cars that cost and equal amount or more = .9772

59Percentile rank = 97.72

d. z = -3.14

Percentile rank = .08

e. z = -3.14, z = +2.0

Proportion between = .4992 + .4772 = .9764

f. 16th percentile converts to a z-score of -.99

-.99(3500) + 23,000 = $19,535

8. a. z = +1.33

Proportion drinking equal to or more = .0918.

b. z = -2.0

Proportion drinking equal to or more = .9772.

c. z = -2.0, z = +1.33

Proportion between = .4772 + .4082 = .8854.

d. 60th percentile converts to a z-score of +.25

.25(1.5) + 5 = 5.375 cups.

e. z = -.67

Percentile rank = 25.14

f. z = +1.67

Percentile rank = 95.25

9.

x z-score percentile rank

Ken 73.00 .22 41.29

Drew 88.95 +1.55 93.94

Cecil 83.28 +.92 82.00

Test Items

Multiple Choice Questions

1. A table in which all of the scores are listed along with the frequency with which each occurs is a

_____.

a. bar graph

b. histogram

c. frequency polygon

d. frequency distribution

Answer: d

w2. A table in which the scores are grouped into intervals and listed along with the frequency of scores

in each interval is a _____.

a. bar graph

b. histogram

c. class interval frequency distribution

60d. class interval frequency polygon

Answer: c

3. A categorical variable for which each value represents a discrete category is a _____ variable.

a. qualitative

b. quantitative

c. continuous

d. class interval

Answer: a

4. A variable for which the scores represent a change in quantity is a _____ variable.

a. qualitative

b. quantitative

c. class interval

d. nominal

Answer: b

5. A graphical representation of a frequency distribution in which vertical bars are centered above

each category along the x-axis and are separated from each other by a space, is a _____.

a. histogram

b. bar graph

c. pie graph

d. frequency polygon

Answer: b

6. A graphical representation of a frequency distribution in which vertical bars centered above scores

on the x-axis touch each other is a _____.

a. histogram

b. bar graph

c. pie graph

d. frequency polygon

Answer: a

w7. A line graph of the frequencies of individual scores is a _____.

a. histogram

b. frequency distribution

c. frequency polygon

d. bar graph

Answer: c

8. _____ is to organizing data using a table as _____ is to organizing data using a figure.

a. histogram; bar graph

b. frequency polygon; bar graph

c. frequency distribution; histogram

d. frequency polygon; frequency distribution

Answer: c

619. Bar graphs are to _____ as frequency polygons are to _____.

a. quantitative variables; qualitative variables

b. qualitative variables; quantitative variables

c. continuous data; discrete data

d. quantitative variables and continuous data; qualitative variables and discrete data

Answer: b

10. Qualitative variable is to quantitative variable as ____ is to _____.

a. categorical variable; numerical variable

b. numerical variable; categorical variable

c. ordinal, interval, or ratio data; nominal data

d. categorical variable and ordinal, interval, or ratio data; numerical variable and nominal data

Answer: a

11. A number that characterizes the “middleness” of an entire distribution is _____.

a. a measure of central tendency

b. a measure of variability

c. an inferential statistic

d. the standard deviation

Answer: a

w12. The arithmetic average of a distribution is the:

a. mean

b. median

c. mode

d. standard deviation

Answer: a

13. Seven students reported the following individual earnings from their sale of wrapping paper: $7,

$13, $3, $5, $2, $9, and $3. In this distribution of individual earnings, the mean is _____ the

mode and _____ the median.

a. equal to; equal to

b. greater than; equal to

c. equal to; less than

d. greater than; greater than

Answer: d

w14. During the past year, Cindy and Bobby each read 2 books, but Greg read 25, Jan read 12, and

Marcia read 9. The median number of books read by these individuals was:

a. 2.

b. 9.

c. 10.

d. 50.

Answer: b

15. The middle score in a distribution after the scores have been arranged from highest to lowest or

lowest to highest is the _____.

a. mean

b. median

62c. mode

d. standard deviation

Answer: b

16. When Ms. Jones calculated her students’ accounting test scores, she noticed that one student had

an extremely low score. Which measure of central tendency should not be used in this situation?

a. mean

b. standard deviation

c. mode

d. median

Answer: a

17. Imagine that 86,999 people who are penniless live in Centerville. Bill Gates, whose net worth is

$87,000,000,000 moves to Centerville. Now the mean net worth in this town is _____ and the

median net worth is _____.

a. 0; 0

b. 0; $1,000,000

c. $1,000,000; 0

d. $1,000,000; $1,000,000

Answer: c

18. Arithmetic average is to _____ as score occurring with the greatest frequency is to _____.

a. mean; median

b. median; mode

c. mean; mode

d. mode; median

Answer: c

w19. a. b. c. d. Mode is to _____ as median is to _____.

interval and ratio data only; nominal data only

nominal data only; ordinal data only

all types of data; ordinal, interval, and ratio data only

none of the alternative is correct

Answer: c

20. A distribution can have more than one ____ but can have only one _____.

a. median; mode or mean

b. mean; mode or median

c. mode; median or mean

d. median or mode; mean

Answer: c

21. Which of the following is a disadvantage of using the range as a measure of variation?

a. b. c. d. It is limited because only two of the scores in the distribution are used to derive it.

It is easily distorted by an unusually high or low score in a distribution.

It can only be used with nominal data.

It is limited because only two of the scores in the distribution are used to derive it and it is

easily distorted by an unusually high or low score in a distribution.

63Answer: d

22. The calculation of the average deviation differs from the calculation of the standard deviation in

that the difference scores are:

a. squared.

b. converted to absolute values.

c. squared and converted to absolute values.

d. it does not differ.

Answer: b

23. Imagine that distribution A contains the following scores: 3, 4, 5, 6, 7. Imagine that distribution B

contains the following scores: 1, 3, 5, 8, 10. Distribution A has a _____ standard deviation and a

_____ average deviation in comparison to distribution B.

a. larger; larger

b. smaller; smaller

c. larger; smaller

d. smaller; larger

Answer: b

24. Which of the following is NOT TRUE?

a. The range is a simplistic measure of variation that does not use all scores in the distribution

in its calculation.

b. The average deviation is a more sophisticated measure of variation than the range in which

all scores are used, but which may not weight extreme scores adequately.

c. The standard deviation is the least sophisticated measure of variation and the least

frequently used.

d. All of the alternatives are true.

Answer: c

w25. If the shape of a frequency distribution is lopsided, with a long tail projecting longer to the right

than to the left, how would the distribution be skewed?

a. normally

b. negatively

c. positively

d. average

Answer: c

26. A z-score is most affected by the:

a. median

b. mode

c. standard deviation

d. range

Answer: c

27. If Joe scored 25 on a test with a mean of 20 and a standard deviation of 5 what is his z-score?

a. 25

b. +1.0

c. 0.0

d. cannot be determined

64Answer: b

28. Sue took a test in both biology and math last week. The biology test had a mean of 70 and a

standard deviation of 7 whereas the math test had a mean of 75 and a standard deviation of 10. Sue

scored a 76 on the biology test and a 76 on the math test. On which test did she do better in

comparison to the rest of the class?

a. the math test

b. the biology test

c. she did the same on each test

d. cannot be determined

Answer: b

W29. Faculty in the psychology department at State University consume an average of 5 cups of coffee

per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty

consume an amount between 4 and 6 cups?

a. .5468

b. .4972

c. .50

d. none of the alternative is correct

Answer: b

30. Faculty in the psychology department at State University consume an average of 5 cups of coffee

per day with a standard deviation of 1.5. The distribution is normal. What is the percentile rank for

an individual who consumed 8 cups of coffee per day?

a. 97.72

b. 2.28

c. 47.72

d. none of the alternatives is correct

Answer: a

31. Faculty in the psychology department at State University consume an average of 5 cups of coffee

per day with a standard deviation of 1.5. The distribution is normal. How many cups of coffee

would an individual at the 25th percentile drink per day?

a. 4

b. 5

c. 6

d. 7

Answer: a

32. If the average height for women is normally distributed with a mean of 65 inches and a standard

deviation of 2.5 inches, then approximately 95% of all women should be between _____ and

_____ inches in height.

a. 62.5; 67.7

b. 60; 70

c. 57.5; 72.5

d. Cannot say from the information given.

Answer: b

w33. Rich’s first psychology exam score is +1 standard deviation from the mean in a normal

distribution. The test has a mean of 60 and a standard deviation of 6. Rich’s percentile rank would

65be approximately:

a. 70%.

b. 84%.

c. 66%.

d. Cannot say from the information given.

Answer: b

34. Approximately what percentage of scores are between z=1 and z=2?

a. 50

b. 68

c. 16

d. 13.5

Answer: d

35. Karen’s first psychology exam score is -1 standard deviation from the mean in a normal

distribution. The test has a mean of 75 and a standard deviation of 5. Karen’s percentile rank

would be:

a. 16%.

b. 54%.

c. 70%.

d. cannot say from the information given

Answer: a

36. In a psychology class of 100 students, test scores are normally distributed with a mean of 80 and a

standard deviation of 5. Approximately what percentage of students have scores between 70 and

90?

a. 68%

b. 80%

c. 95%

d. 99%

Answer: c

Short Answer/Essay Questions

1. Draw the frequency polygon for the following sample distribution (there are 30 scores in the

distribution). In addition calculate the mean, median and mode for the distribution.

48, 50, 53, 59, 59, 63, 63, 67, 67, 67, 72, 72, 72, 78, 78, 78, 78, 85, 85, 85, 85, 85, 90, 90, 90, 90,

95, 95, 98, 100

666

5

4

Frequency

3

2

1

0

48 53 63 72 85 95 100

Variable A

2. 3. 4. 5. 6. Explain the difference between qualitative and quantitative variables noting the relationship of

nominal, ordinal, interval, and ratio data to these terms.

A qualitative variable is a categorical variable for which each value represents a discrete

category, whereas a quantitative variable is a variable for which the scores represent a change in

quantity. Nominal data are qualitative and ordinal, interval, and ration data are quantitative.

Explain the difference in proper use between a bar graph and a histogram.

A bar graph is used when the data are nominal and qualitative. A histogram is used when the data

are qualitative and ordinal, interval, o ratio.

Calculate the mean, median, and mode for the following sample: 2, 2, 6, 9, 10, 11, 15, 17, 18, 20.

The mean is 11, the median is 10.5, and the mode is 2.

For a hypothetical normal distribution of test scores, approximately 95% fall between 38 and 62,

2.5% are below 38 and 2.5% are above 62. Given this information, (a) the mode = _________ and

(b) the standard deviation = _________.

The mode is 50 (along with the mean and median) and the standard deviation is 6.

Calculate s (standard deviation) and A.D. (average deviation) for the following sample.

2, 2, 6, 9, 10, 10, 15, 18, 18, 20.

The standard deviation is 6.56 and the A.D. is 5.4.

677. Draw a positively skewed distribution and a negatively skewed distribution noting where the

mean, median, and mode would fall with respect to each other in these distributions.

Negatively Skewed Positively Skewed

8. Tom, Tina, & Tori took a verbal aptitude test. The test was normally distributed with a mean

of 70 and s = 15. Complete the following table.

Name Raw Score Z score Percentile Rank

Tom 73 +.20 57.93

Tina 52 1.2 11.51

Tori 58.9 .74 23

9. Students in the psychology department consume

an average of 5 cups of coffee per day with a standard deviation of 1.75 cups. The number of cups

of coffee consumed is normally distributed.

 What proportion of students consume an amount equal to or less than 6 cups per day?

.7157

 How many cups would an individual at the 80th percentile drink?

6.47

10. Draw two distributions with the same standard deviations but different means.

68