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Set A: {1, 3, 5, 7, 9}
Set B: {102, 103, 104, 105, 106}
Set C: {-15, -12, -9, -6, -3}
Which of the following properly ranks the sets in terms of their standard deviation, from greatest to least?
A. B, A, C
B. B, C, A
C. A, C, B
D. C, B, A
E. C, A, B
Set B: {102, 103, 104, 105, 106}
Set C: {-15, -12, -9, -6, -3}
Which of the following properly ranks the sets in terms of their standard deviation, from greatest to least?
A. B, A, C
B. B, C, A
C. A, C, B
D. C, B, A
E. C, A, B
kungfury42
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04 Feb 2022, 02:44
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Two ways of doing this question, the first one is to actually calculate the values of Standard Deviation for the three sets and compare, but we'll not get into it, instead we'll use the second method that involves observing the spread of the numbers.
Set A: All the numbers are uniformly spread and have a distance of 2 units from each other. The middle number is the mean. The corner numbers are at a distance of 4 units from the mean and the ones adjacent to them are at a distance of 2 units from the mean.
Set B: All the numbers are uniformly spread and have a distance of 1 units from each other. The middle number is the mean. The corner numbers are at a distance of 2 units from the mean and the ones adjacent to them are at a distance of 1 units from the mean.
Set C: All the numbers are uniformly spread and have a distance of 3 units from each other. The middle number is the mean. The corner numbers are at a distance of 6 units from the mean and the ones adjacent to them are at a distance of 3 units from the mean.
Since standard deviation is the measure of how far the numbers are spaced with regard to the mean, we can see that Set C has the greatest standard deviation, followed by set A, and then by set B.
Hence, the order from greatest to lowest should be C, A, B. Option E.
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Set A: All the numbers are uniformly spread and have a distance of 2 units from each other. The middle number is the mean. The corner numbers are at a distance of 4 units from the mean and the ones adjacent to them are at a distance of 2 units from the mean.
Set B: All the numbers are uniformly spread and have a distance of 1 units from each other. The middle number is the mean. The corner numbers are at a distance of 2 units from the mean and the ones adjacent to them are at a distance of 1 units from the mean.
Set C: All the numbers are uniformly spread and have a distance of 3 units from each other. The middle number is the mean. The corner numbers are at a distance of 6 units from the mean and the ones adjacent to them are at a distance of 3 units from the mean.
Since standard deviation is the measure of how far the numbers are spaced with regard to the mean, we can see that Set C has the greatest standard deviation, followed by set A, and then by set B.
Hence, the order from greatest to lowest should be C, A, B. Option E.
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