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A certain data set has n numbers, an average (arithmetic mean) of 5, a

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A certain data set has n numbers, an average (arithmetic mean) of 5, a  [#permalink]

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New post 11 Jan 2017, 03:47
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E

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Question Stats:

69% (01:30) correct 31% (02:00) wrong based on 86 sessions

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A certain data set has n numbers, an average (arithmetic mean) of 5, and a standard deviation of s. If n and s are positive, which of the following pairs of numbers, when added to the data set, must result in a set with n + 2 numbers and a standard deviation less than s?

A. -5 and 0
B. 0 and 0
C. 0 and 5
D. 0 and 10
E. 5 and 5

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Re: A certain data set has n numbers, an average (arithmetic mean) of 5, a  [#permalink]

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New post 11 Jan 2017, 03:55
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[quote="Bunuel"]A certain data set has n numbers, an average (arithmetic mean) of 5, and a standard deviation of s. If n and s are positive, which of the following pairs of numbers, when added to the data set, must result in a set with n + 2 numbers and a standard deviation less than s?

A. -5 and 0
B. 0 and 0
C. 0 and 5
D. 0 and 10
E. 5 and 5

Answer is Option E
Reason:-
Thumb Rule---Standard deviation in a set of numbers is decided by the NUMBERS within the set.
If the numbers are very far away from the mean then the standard deviation rises and if numbers are closer to the mean the standard deviation comes down.

Now in the given question we need to add two nos so that the standard deviation comes below the given standard deviation, SO TRY ADDING NUMBERS WHICH ARE AS CLOSE AS POSSIBLE TO THE MEAN...!!

In the given options Only E option satisfies. Both the numbers are equal to the mean...
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Re: A certain data set has n numbers, an average (arithmetic mean) of 5, a  [#permalink]

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New post 16 Dec 2019, 09:04
Just want to say that the other way of reducing the SD is to increase the denominator of the SD eq ( n to n+2) with simultaneous decrease/no change in the numerator ( 5-5=0, 5-5=0). Choice E does both .
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Re: A certain data set has n numbers, an average (arithmetic mean) of 5, a   [#permalink] 16 Dec 2019, 09:04
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