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The data sets I, II, and III above are ordered from...

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The data sets I, II, and III above are ordered from...

by swerve » Wed Jan 31, 2018 5:25 am
I. a-14, a, a, a, a+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c

The data sets I, II and III above are ordered from greatest standard deviation to least standard deviation in which of the following?

A. I, II, III
B. I, III, II
C. II, III, I
D. III, I, II
E. III, II, I

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
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by regor60 » Wed Jan 31, 2018 8:07 am
swerve wrote:I. a-14, a, a, a, a+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c

The data sets I, II and III above are ordered from greatest standard deviation to least standard deviation in which of the following?

A. I, II, III
B. I, III, II
C. II, III, I
D. III, I, II
E. III, II, I

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
The standard deviation indicates dispersion of the elements around their mean.

A quick glance at III shows that since all the elements are the same, their mean is the same and there is no difference between any element and the mean, so 0 dispersion.

Since the question asks for highest to lowest ordering by standard deviation, clearly III is last. The only answer choice with III as last is A. No calculations required.
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by DrMaths » Wed Jan 31, 2018 8:13 am
swerve wrote: I. a-14, a, a, a, a+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c

The data sets I, II and III above are ordered from greatest standard deviation to least standard deviation in which of the following?

A. I, II, III
B. I, III, II
C. II, III, I
D. III, I, II
E. III, II, I

The OA is A.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
Standard Deviation is a quantity that expresses by how much the members of a group differ from the mean value for the group.
Now look at the sets. All have the same number of values, n = 5, so that can be ignored. Also the formula for SD requires a square root, but as this is applied for all 3 sets, we can ignore the square root too. We don't need the actual SD, only comparison of magnitude between them.
So we can use an abridged formula, C = Sum of squares of (term - mean)

Also, common terms can be subtracted, as we are only interested in the differences:

I. a-14, a, a, a, a+14 -> -14,0,0,0,14 -> , mean = 0, C = (-14)^2 + 0 + 0 + 0 + 14^2 = 2*14^2 = 392
II. b, b+1, b+2, b+3, b+4 -> 0,1,2,3,4 -> mean = 2, C = (-2)^2 + (-1)^2 + 0 + 1^2 + 2^2 = 10
III. c, c, c, c, c -> 0,0,0,0 -> mean = 0, C = 0

Hence the order is I, II,III

Note however, that you don't even need to calculate the full answers as it is easy to know that 14^2 is significantly higher than 2^2.
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