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The standard deviation of a list of 11 different integers,
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28 Aug 2020, 10:19
28 Aug 2020, 10:19
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94% (00:28) correct
5% (00:43) wrong based on 37 sessions
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Quantity A |
Quantity B |
The standard deviation of a list of 11 different integers, each of which is between 1 and 30, inclusive |
The standard deviation of a list of 11 different integers, each of which is between 31 and 60, inclusive |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: The standard deviation of a list of 11 different integers,
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28 Aug 2020, 10:24
28 Aug 2020, 10:24
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Re: The standard deviation of a list of 11 different integers,
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29 Aug 2020, 09:33
29 Aug 2020, 09:33
1
Carcass wrote:
Quantity A |
Quantity B |
The standard deviation of a list of 11 different integers, each of which is between 1 and 30, inclusive |
The standard deviation of a list of 11 different integers, each of which is between 31 and 60, inclusive |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Remind the following property about standard deviation.
If differences of consecutive data in one set \(X\) are wider than differences on consecutive data in other set \(Y\), then the standard deviation of the former set \(X\) is greater than the standard deviation of the latter set \(Y\) and we have \(SD(X) > SD(Y)\).
Consider two cases.
Case 1: \(A = \{ 1, 2, 3, \cdots , 11 \}\) and \(B = \{ 31, 33, 35, \cdots , 51 \}\).
The differences of consecutive elements in the set \(A\) are \(2 - 1 = 3 - 2 = \cdots = 11 - 10 = 1\).
The differences of consecutive elements in the set \(B\) are \(33 - 31 = 35 - 33 = \cdots = 51 - 49 = 2\).
Thus, we have \(SD(A) < SD(B)\).
Case 2: \(A = \{ 1, 3, 5, \cdots , 21 \}\) and \(B = \{ 31, 32, 33, \cdots , 41 \}\).
The differences of consecutive elements in the set \(A\) are \(3 - 1 = 5 - 3 = \cdots = 21 - 19 = 2\).
The differences of consecutive elements in the set \(B\) are \(32 - 31 = 33 - 32 = \cdots = 41 - 40 = 1\).
Thus, we have \(SD(A) > SD(B)\).
Therefore, D is the right answer.
