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Measures of Central Tendency and Variability
1. One semester, a statistics professor gave five exams to the class. In an effort to get the students to
apply what they have learned in their statistics classes they are told that the final course grade will
be based on the central tendency of their choice. Below are the scores for three of the students.
Which method would you suggest that each one choose (assuming that you want them all to get
high grades)?
1
35
10
56
Andrew
Katherine
Shannon
Examination
3
65
65
67
2
40
50
56
4
90
80
78
5
90
85
98
2. Some researchers in understanding g-loads on humans are interested in methods that can be used
to assist pilots withstand g-load. To study this in a controlled environment, they need to develop a
standardized way to safely measure g-loads in the research participants. One way that they can do
this is to have participants experience a g-load and give them a simple calculation to perform. This
was repeated three times for each participant and the results are shown in the table below.
Calculate the mean, mode and median for each.
Attempt
1
Attempt
2
Attempt
3
Time in Seconds (s)
37
43
30
35
39
38
30
20
28
26
29
60
21
45
23
57
50
47
52
38
41
52
25
44
37
30
28
57
29
25
20
53
50
30
52
60
Measures of Variance and Standard Deviation
3. As part of an assessment for navigation, a professor has his students take a written test. He
teaches two sections of the class. The scores from the students in each section appear below.
Compute the variance and standard deviations for test 1 and test 2 shown below in the table. What
do the results say about the relative homogeneity of the two classes? Assume these are samples of
a much larger population.
Test 1
Test 2
110
100
125
97
78
108
Test Score
87
63
101
86
135
91
90
95
51
100
4. Below in the table is the data from Set 1 of training airport security guards. In this study, participants
were to identify how many security risks they could identify. The researcher recorded how many
they identified. Assume this data reflects a sample.
• Calculate the standard deviation for this set of scores.
• Explain what the standard deviation means in this context. (Explain it as though you are
telling someone that knows nothing about statistics — i.e., make it sound simple.)
Recorded Risks
Set 35 39 38 30 37 43 30 38 41 52 25 44
1
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