Check all that apply. Which of these is a way to define the center of a distribution?
The three ways to define central tendency are: the point at which a distribution is balanced, the number which minimizes
the sum of the absolute differences, and the number which minimizes the sum of the squared differences.
true
the balancing point on a scale
true
the smallest absolute deviation
true
the smallest squared deviation
false
the average of the minimum and maximum
You just took a test and got a 75%. Three possibilities of how the rest of the class performed on this test appear below.
In which of the three possibilities did you score well above the center of the distribution?
In Outcome B, your score is higher than all but one of the rest of the scores. Just by looking at the distribution, you can tell that you did very well compared to the rest of the class. Thus, you scored well above the center of the distribution.
false
Outcome A
In Outcome A, you did about average, with your score falling in the middle of the group. This puts you about at the center of the distribution.
true
Outcome B
false
Outcome C
In Outcome C, you did worse than almost everyone else. This puts you below the center of the distribution.
test_outcomes.gif
For the numbers 10, 12, 16, and 20, the sum of the absolute deviations from 15 is:
14
0.0
Subtract 15 from each number, take the absolute value of the differences, and add them together.
|10-15| + |12-15| + |16-15| + |20-15| = 5 + 3 + 1 + 5 = 14
Which of these numbers minimizes the sum of the absolute deviations for the numbers 4, 9, 12, 15, and 16?
The sum of the absolute deviations from each choice is: 10-20, 11-19, 12-18, 13-19. Thus, the sum of absolute deviations from 12 is the smallest.
(This number 12 is also the median.)
false
10
false
11
true
12
false
13
To balance a distribution, the fulcrum goes in the geometric center of the scale. This is true for every type of distribution.
Only a symmetric distribution is balanced when the fulcrum is in the geometric middle. The fulcrum needs to be placed elsewhere for an asymmetric distribution to balance.
false
True
true
False
For the numbers 3, 6, 9, and 10, the sum of the squared deviations from 8 is:
34
0.0
Subtract 8 from each number, square the differences, and add them together.
(3-8)^2 + (6-8)^2 + (9-8)^2 + (10-8)^2 = 25 + 4 + 1 + 4 = 34