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Set A consists of five different numbers; set B consists of

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Set A consists of five different numbers; set B consists of  [#permalink]

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Set A consists of five different numbers; set B consists of four different numbers, each of which is in set A. Is the standard deviation of set A less than the standard deviation of set B ?

(1) Set A contains five consecutive integers.

(2) The average (arithmetic mean) of set A is equal to the average (arithmetic mean) of set B.


How do you solve statement 2 I landed on one lucky example( set A 0 10 20 30 40 and set B 0 10 30 40) and guessed it to be sufficient. Can someone provide a detailed analysis... Thanks!
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Re: Set A consists of five different numbers; set B consists of  [#permalink]

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New post 12 Jul 2013, 08:31
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Set A consists of five different numbers; set B consists of four different numbers, each of which is in set A. Is the standard deviation of set A less than the standard deviation of set B ?

(1) Set A contains five consecutive integers. A={1, 2, 3, 4, 5} and B={1, 2, 4, 5}, then SD(A)<SD(B) (since A is obtained by adding the element equal to the mean to set B) but if A={1, 2, 3, 4, 5} and B={1, 2, 3, 4}, then SD(A)>SD(B) (since B is less widespread than A). Not sufficient.

(2) The average (arithmetic mean) of set A is equal to the average (arithmetic mean) of set B. If we add to a set new element, which is equal to the mean of the original set, then the standard deviation decreases (well if the SD was not 0). We know that A is obtained by adding one element to set B. Since doing so the mean of A does not change, then we added the element which was equal to the mean, thus we decreased the standard deviation --> SD(A)<SD(B). Sufficient.

Answer: B.

Hope it's clear.
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