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07 Nov 2020, 11:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
72% (00:46) correct
28%
(01:11)
wrong
based on 68
sessions
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Set A: {-11, 0, 0, 11}
Set B: {2, 4, 6, 8}
Set C: {50, 51, 52, 53}
Set D: {12, 12, 12, 12}
Which of the following sets have a maximum & minimum standard deviation respectively?
A. Max: A, Min: B
B. Max: B, Min: C
C. Max: C, Min: D
D. Max: B, Min: D
E. Max: A, Min: D
Set B: {2, 4, 6, 8}
Set C: {50, 51, 52, 53}
Set D: {12, 12, 12, 12}
Which of the following sets have a maximum & minimum standard deviation respectively?
A. Max: A, Min: B
B. Max: B, Min: C
C. Max: C, Min: D
D. Max: B, Min: D
E. Max: A, Min: D
07 Nov 2020, 12:06
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Bunuel
A set who's values are the furthest from the mean will have the maximum standard deviation and those who are the least away from the mean will have the least standard deviation.
With this Set D will have the least standard deviation and will be equal to 0.
Set A will have the maximum standard deviation as its means = 0, is far away from -11 and 11.
\(SD = \sqrt{\frac{SUM(x - \bar{x})^2}{n}}\), where \(\bar{x}\) is the mean of the set
For Set A: Mean = 0,
SUM\((x - \bar{x})^2 = (-11 - 0)^2 + (0 - 0)^2 + (0 - 0)^2 + (11 - 0)^2 = 121 + 0 + 0 + 121 = 242\)
\(SD = \sqrt{\frac{242}{4}} = \sqrt{60.5}\)
For Set B: Mean = 5,
SUM\((x - \bar{x})^2 = (2 - 5)^2 + (4 - 5)^2 + (6 - 5)^2 + (8 - 5)^2 = 9 + 1 + 1 + 9 = 20\)
\(SD = \sqrt{\frac{20}{4}} = \sqrt{5}\)
For Set C: Mean = 51.5,
SUM\((x - \bar{x})^2 = (50 - 51.5)^2 + (51 - 51.5)^2 + (52 - 51.5)^2 + (53 - 51.5)^2 = 2.25 + 0.25 + 0.25 + 2.25 = 5\)
\(SD = \sqrt{\frac{5}{4}} = \sqrt{1.25}\)
For Set D: Mean = 12,
SUM\((x - \bar{x})^2 = (12 - 12)^2 + (12 - 12)^2 + (12 - 12)^2 + (12 - 12)^2 = 0 + 0 + 0 + 0 = 0\)
\(SD = \sqrt{\frac{0}{4}} = \sqrt{0} = 0\)
Option E
Arun Kumar
08 Nov 2020, 13:50
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Bunuel
The standard deviation is a measure of how spread apart the data points are.
Set D has an STD of 0 since the points are all the same, so the min must be D.
Set B and C have relatively close points, so they have a small standard deviation but set B's is a bit higher.
Set A has two very far away points so it likely has the highest standard deviation, the only possible competitor is set B. If the student is low on time the best guess would be E here.
To compare the standard deviations of two sets with the same number of elements, we can subtract the average and then look at the sum of the data points squared.
After subtracting the mean A is {-11, 0, 0, 11} and B is {-2, -1, 1, 2}, square the data points and then add the values. A has a sum of 121+121 while B has a sum of only 4+1+1+4 so A has a much higher standard deviation.
Ans: E
