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# What is the standard deviation of a set of 7 numbers whose mean is 20?

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Math Expert
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What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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21 Mar 2017, 04:56
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Question Stats:

45% (01:27) correct 55% (01:50) wrong based on 134 sessions

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What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.

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Re: What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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30 Oct 2017, 08:50
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Bunuel wrote:
What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.

Hi...
there has been some confusion over the solution, so let me pitch in..

there are 7 numbers and mean is 20

lets see the statements-

(1) The absolute value of the difference of each number in the set from the mean is equal.
Since it talks of EACH number from mean is equal, the first thing you should realize is that MEAN is NOT in the set if numbers are different OR all are equal to mean
lets see these two cases-
A) All are equal to MEAN that is 20 so 20,20,20,20,20,20,20... SD will be 0
B) Mean is not in the set - Since there are ODD elements in the set, MEAN will never be 20..
say 3 are 1 above mean, the other 3 will cover up by being 1 below mean but what about 7th - it has to be EQUAL to mean to keep the mean as 20
as per statement I , set will be 19,19,19,19,21,21,21 or 19,19,19,21,21,21,21 but in each case mean will not be 20
so ONLY possibility is 20,20,20,20,20,20,20 and SD will be 0...
suff

(2) The sum of the squares of the differences from the mean is greater than 100.
clearly insuff

A
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What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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21 Mar 2017, 05:06
since there are 7 numbers in the set, I believe it's A.
all numbers are 20, thus, SD is 0
were there 2, 4, 6, 8 numbers - i think it would have been E.
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Re: What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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21 Mar 2017, 21:36
first lets understand how SD is calculated..

stat 1: it says absolute value is same. but no information about abs value is given.
hence not suff

stat 2: it only says sum is greater than 100.. it can be 110, 120 ,,anything above 100..not suff

both combined not suff.

hence E
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Re: What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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29 Oct 2017, 23:43
Please elaborate How is only A sufficient?

I thought for it the following way:
(A) given that the difference from mean is same, means SD is one fixed value. for example, the {15,15,15,20,25,25,25} with sd=5 OR {10,10,10,20,30,30,30} with sd=10
standard deviation is variable, hence not sufficient.

(B) the sum greater than 100 could be anything, 101 or 500 or 5000.
Hence, not sufficient.

The correct answer seems to be E.
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Re: What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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30 Oct 2017, 09:12
Thanks chetan2u!
I think i understood it now. I need to read the question very carefully and pay attention to the words. Thanks again!
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Re: What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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09 Nov 2017, 11:18
chetan2u wrote:
Bunuel wrote:
What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.

Hi...
there has been some confusion over the solution, so let me pitch in..

there are 7 numbers and mean is 20

lets see the statements-

(1) The absolute value of the difference of each number in the set from the mean is equal.
Since it talks of EACH number from mean is equal, the first thing you should realize is that MEAN is NOT in the set if numbers are different OR all are equal to mean
lets see these two cases-
A) All are equal to MEAN that is 20 so 20,20,20,20,20,20,20... SD will be 0
B) Mean is not in the set - Since there are ODD elements in the set, MEAN will never be 20..
say 3 are 1 above mean, the other 3 will cover up by being 1 below mean but what about 7th - it has to be EQUAL to mean to keep the mean as 20
as per statement I , set will be 19,19,19,19,21,21,21 or 19,19,19,21,21,21,21 but in each case mean will not be 20
so ONLY possibility is 20,20,20,20,20,20,20 and SD will be 0...
suff

(2) The sum of the squares of the differences from the mean is greater than 100.
clearly insuff

A

Hi chetan2u Bunuel

Statement 1, difference between any value and mean is equal. This is possible only when all the elements in the set are same. So SD = sq.root of (sum of squares of differences of each value from mean)/7 = 0 -> sufficient.

However, statement 2, says sum of squares of differences of each value from mean > 100. I am not sure how it is possible.
From statement 1, we get all elements are same, but statement2 is contradicting.

So i was scratching my head

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Re: What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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11 Oct 2018, 18:02
Bunuel wrote:
What is the standard deviation of a set of 7 numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal.

(2) The sum of the squares of the differences from the mean is greater than 100.

I chose E at first, but would agree A is correct answer. Note that (1) says "The absolute value of the difference of each number in the set from the mean is equal." , the value of the difference of each number from the mean has to be 0, i.e., all 7 numbers are 20, thus SD is 0.
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Re: What is the standard deviation of a set of 7 numbers whose mean is 20?  [#permalink]

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08 Feb 2019, 06:19
Please elaborate How is only A sufficient?

I thought for it the following way:
(A) given that the difference from mean is same, means SD is one fixed value. for example, the {15,15,15,20,25,25,25} with sd=5 OR {10,10,10,20,30,30,30} with sd=10
standard deviation is variable, hence not sufficient.

(B) the sum greater than 100 could be anything, 101 or 500 or 5000.
Hence, not sufficient.

The correct answer seems to be E.

I have this same doubt can anyone explain ?
Re: What is the standard deviation of a set of 7 numbers whose mean is 20?   [#permalink] 08 Feb 2019, 06:19
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