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Practice Problem #1

Chief Smith is interested in determining how his officers are performing on their annual firearms recertification exam. He has sent 10 officers through the testing and their scores are presented below. Scores on the exam range from 1 to 10, with 1 being unacceptable and 10 being perfect. Answer the following questions based upon these test scores.

10

10

10

8

7

6

4

2

1

2

What is the Mean of the above scores? What is the Median? What is the Mode?

Is this distribution Normal or Skewed? If it is skewed, then is it skewed positive or negative?

What is the Range for the above Distribution? What is the standard deviation? What is the variance?

 

 

Practice Problem # 2

Chief Campbell has conducted a separate study on a criminal procedure examination. She has found that the data set forms a normal distribution. She has also found the following values:

The mean is 73 and the standard deviation is 8.

She is now concerned with discovering what percentage of scores are falling between -2 and +2 standard deviation units? At -2 what is the lowest that someone should score? At +2 what is the highest that someone should score?

 

Practice #3

A young intern has brought you a listing of inmate IQ scores for individuals housed within the disciplinary unit. You have been tasked with examining these scores. Which of the following is the most frequently occurring value (Hint: develop a frequency distribution)? What does the histogram look like? What does the asterisks graph look like?

80

75

73

85

86

76

80

79

78

89

95

85

94

97

105

115

81

80

111

100

93

92

Answers to Practice Problems

Problem #1

What is the Mean of the above scores? 6 What is the Median? 6.5 What is the Mode? 10

Is this distribution Normal or Skewed? Skewed If it is skewed, then is it skewed positive or negative? Negative

What is the Range for the above Distribution? 8 What is the standard deviation? 3.38 What is the variance? 11.4

 

Problem #2

She is now concerned with discovering what percentage of scores are falling between -2 and +2 standard deviation units? 94-95% (Depending upon whether we round the percentages off or carrying them out)

At -2 what is the lowest that someone should score? 57 At +2 what is the highest that someone should score? 89

Problem #3

X

F
73 1
75 1
76 1
78 1
79 1
80 3
81 1
85 2
86 1
89 1
92 1
93 1
94 1
95 1
97 1
100 1
105 1
111 1
115 1

80 is the most commonly occurring IQ score.

 

Asterisks Graph *If you want to check your histogram graph come by my office and we will go over one.

X

F
73 *
75 *
76 *
78 *
79 *
80 ***
81 *
85 **
86 *
89 *
92 *
93 *
94 *
95 *
97 *
100 *
105 *
111 *
115 *