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Answer all questions on the document attached below. You may need the program stat crunch or similar to answer ATTACHED QUESTIONS.
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RSCH 665 – Module 2 Assignment
Measures of Central Tendency and Variability
1. One semester, a statistics professor gave six 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 for each student will be based on the central tendency measurement
of their choice. Below are the scores for three of the students. Calculate the mean, mode
and median for each student and present in a table. Which measure of central tendency
would you suggest that each one choose?
Test 1
94
84
92
Emmett
Kiernan
Brennan
Test 2
74
83
68
Examination
Test 3
Test 4
63
59
73
80
69
82
Test 5
74
88
92
Test 6
92
80
78
Emmett?
Kiernan?
Brennan?
Measures of Variance and Standard Deviation
2. As part of an assessment for navigation, a professor has his students take a written test.
He teaches five sections of the class. The scores from the students in each section
appear below. Compute the mean, variance, and standard deviations for each class
shown below in the table. **Assume these students are the entire population. (This is a
clue – check your StatCrunch videos for the differences in how to calculate standard
deviation for a sample and a population.)
Class
1
2
3
4
5
A
94
89
93
85
82
B
84
79
92
74
100
C
74
84
91
93
85
Student Scores
D
E
F
54
84
92
77
79
73
87
84
88
91
93
98
78
68
68
G
71
77
81
94
99
H
63
71
73
70
90
I
92
96
77
86
90
Class 1:
Class 2:
Class 3:
Class 4:
All rights are reserved. The material contained herein is the copyright property of Embry-Riddle Aeronautical University, Daytona
Beach, Florida, 32114. No part of this material may be reproduced, stored in a retrieval system or transmitted in any form,
electronic, mechanical, photocopying, recording or otherwise without the prior written consent of the University.
College of Aeronautics | worldwide.erau.edu
Class 5:
3. Below in the table is the data from Set 1 of training 24 airport security guards. In this
study, participants were asked to identify security risks. The researcher recorded how
many they identified. Assume this data reflects a sample. Calculate the mean, variance,
and standard deviation for this set of scores. Explain the difference between the
standard deviation of these scores (a sample) and standard deviation of a population.
9
18
7
16
32
14
14
7
1
Risks Identified
10
24
18
38
3
12
5
7
16
25
22
23
19
11
10
The table below will be used for the following five questions. The table represents the mean and
standard deviation graduation rates, by candidate age, for a population of flight academies.
Here is an electronic version of the Z-table. (Each subquestion = 5 points for a total of 25 points)
Age
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Mean Graduation Rate
75.6
80
78.5
78.6
82.2
85.2
86.5
89.5
87.5
86.7
87.8
87.1
88.8
91.1
84.8
87.3
87.3
82.5
83.1
89.1
88.2
85.5
81.5
84.8
84.4
Standard Deviation
1.8
2.1
1.4
2.5
2.5
2.2
2.0
1.2
1.8
1.7
1.3
1.9
2.8
1.0
2.8
2.2
1.4
2.0
1.3
1.7
1.7
1.2
2.0
1.9
1.6
All rights are reserved. The material contained herein is the copyright property of Embry-Riddle
Aeronautical University, Daytona Beach, Florida, 32114. No part of this material may be reproduced,
stored in a retrieval system or transmitted in any form, electronic, mechanical, photocopying,
recording or otherwise without the prior written consent of the University.
College of Aeronautics | worldwide.erau.edu
a. A flight academy has a graduation rate of 72.1 among all their 17-year old candidates
from the last five years. What percentage of flight academies have a higher graduation
rate for 17-year old candidates?
b. A flight academy has a graduation rate of 83.5 among all their 34-year old candidates
from the last eight years. What percentage of flight academies have a lower graduation
rate for 34-year old candidates?
c. A flight academy boasts it is among the top 10% for graduation rates among its 29-year
old candidates. This academy’s graduation rate is 93.1 over the last two years for 29year old candidates. Is the claim that this flight academy is in the top 10% a true
statement? Explain.
d. A flight academy wants to invest in new training methods to improve its graduation rate
of 18-year old candidates. This academy’s graduation rate for 18-year old candidates is
82.6 for the past ten years. Should the academy invest in the new training methods?
Explain.
e. A flight academy had a graduation rate of 85.1 for 27-year old candidates from 20002009. Since then, new instructors have been hired that have specifically worked on
providing clearer instruction to pilot candidates. From 2010-2018, the graduation rate for
27-year old candidates is 88.3. What percentile did the organization start at from 20002009, and what percentile is the organization now (2010-2018)? Explain what this
means in terms of percentage of population between these scores.
All rights are reserved. The material contained herein is the copyright property of Embry-Riddle
Aeronautical University, Daytona Beach, Florida, 32114. No part of this material may be reproduced,
stored in a retrieval system or transmitted in any form, electronic, mechanical, photocopying,
recording or otherwise without the prior written consent of the University.
College of Aeronautics | worldwide.erau.edu
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