Measures of Central Tendency One semester, a statistics professor gave six tests to the class. In an effort to get the students to apply what they have learned in their statistics classes

Measures of Central Tendency 

 

  1. One semester, a statistics professor gave six tests 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 one of the three central tendency measurements of their choice (mean, median, or mode). Below are the six test scores for three of the students. Which method would you suggest that each one choose (assuming higher percentage is better)? 

 

  Examination
Test 1 Test 2 Test 3 Test 4 Test 5 Test 6
Charlie 74 74 75 85 80 74
Megan 84 84 83 85 97 80
Jorge 92 68 90 92 92 78

 

Charlie?   

 

Megan? 

 

Jorge? 

 

  1. Some researchers wanting to understand g-loads on humans are interested in methods that can be used to assist pilots withstanding g-loads. 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 certain g-load and give them a simple calculation to perform. Nine participants (A thru I) were required to repeat each test three times (attempts) and the results are shown in the table below. Calculate the mean, mode, and median for each for each attempt (row). Assume no units.

 

Attempt Participant
A B C D E F G H I
1 15 18 13 14 15 15 16 17 18
2 12 9 10 11 17 12 16 16 16
3 17 18 18 18 20 21 24 22 21

 

Attempt 1:

Attempt 2:   

Attempt 3: 

 

 

 

Measures of Central Tendency, Variance, and Standard Deviation

 

  1. As part of an assessment for navigation, a professor has his students take a written test. He teaches five different classes (1 thru 5). The scores, (in percentages) 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. Don’t forget units.

 

Class Student Scores
A B C D E F G H I
1 94 84 78 54 82 94 75 83 82
2 89 89 84 74 75 76 77 71 90
3 96 92 91 82 88 88 83 74 67
4 85 77 99 92 91 91 91 72 80
5 89 100 88 73 66 62 95 91 90

 

Class 1:

 

Class 2:

 

Class 3: 

 

Class 4: 

 

Class 5: 

 

 

 

 

  1. Below in the table are data from training 24 randomly chosen airport security guards. In this study, these participants were asked to identify security risks. The researcher recorded how many security risks 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 the standard deviation scores of a population (as indicated in Problem #3). Don’t forget units.

 

Risks Identified
9 13 12 10 4 15 15 14
12 29 5 8 8 14 12 13
10 10 3 7 16 14 13 10