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What is the Standard Deviation of a set of consecutive even integers ?

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What is the Standard Deviation of a set of consecutive even integers ?  [#permalink]

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New post Updated on: 23 Aug 2016, 02:33
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A
B
C
D
E

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What is the Standard Deviation of a set of consecutive even integers ?

(1) There are 39 elements in the set.
(2) the mean of the set is 382.

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Originally posted by hitmoss on 13 May 2011, 07:01.
Last edited by Bunuel on 23 Aug 2016, 02:33, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: What is the Standard Deviation of a set of consecutive even integers ?  [#permalink]

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New post 13 May 2011, 07:19
I am getting an answer C.

st - 1 ==> 39 elements and set of consecutive even integers will not help. You need either the 1st element, last element or the average.
st - 2 ==> you need # of elements; not sufficient.

together ==> mean is 382 so you have (39-1)/2 = 19 elements on each side of 382. Since the integers are consecutive even last element is 382+ 19*2 = 420 and 1st element is 382 -19*2 = 344.
You have 1st element as 344 and you know they are consecutive even integers... so you have all the integers, you have mean so you can find std. deviation.

So both statements are reqd.
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Re: What is the Standard Deviation of a set of consecutive even integers ?  [#permalink]

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New post 13 May 2011, 07:52
1
a for any set of consecutive integers, the standard deviation depends upon the number of elements in the set.

suppose there are two sets - 1,2,3 std deviation = approx 1 (considering only differences from median =2)
1,2,3,4,5 std deviation is stretched as elements 1 and 5 are involved thus its value will be >1 but a fixed value always.

and 6,7,8,9,10 will have same std deviation as set 1,2,3,4,5.


Hence for 39, even numbers where median = 20th elements the std deviation will be a fixed value for any set of numbers meaning -- 2,4,6 or 8,10,12 will have same std deviation. Thus A is sufficient.

b does not give number of elements. set can be 380,382,384 or 378,380,382,384. As mentioned above the std changes.

not sufficient.

Thus A.
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SLIDE #33 in the FlashCards. Standard Deviation  [#permalink]

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New post 09 Oct 2011, 10:55
First of all, I would like to thank all of the GMAT Club team for the amazing effort and dedication it continues to show.
I personally get motivated when I read about the successful GMAT journeys and their after math.

I have a question regarding one of the Standard Deviation examples mentioned in Flash Cards (Slide #33)

What is the Standard Deviation of a set of consecutive even integers?
(1) There are 39 elements in the set.
(2) the mean of the set is 382

Spoiler: :: Doubt
The answer is A, statement (1) is sufficient.

Can some one please explain the logic behind it. I mean how can we get the S.D with out having the actual elements?

Thanks in advance
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Re: SLIDE #33 in the FlashCards. Standard Deviation  [#permalink]

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New post 09 Oct 2011, 19:48
1
I think you missed something in the text as we CAN actually find out the members of the set.

We know that they are consecutive even integers and the mean is 382. That means there are 19 consecutive even integers on the left of this number and another 19 on the right (39 - 1 = 38) and 38/2 = 19.

However in this case, you don't really need to know the actual members of the set since the standard deviation would be known by default regardless of the number values (2, 4, 6, etc) or (20224, 20226, etc). We know that they are spaced within 39*2 = 78 of each other and that's all we need to know. We don't need to calculate the details.

Hope this helps.
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What is the Standard Deviation of a set of consecutive even integers ?  [#permalink]

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New post 12 Jan 2019, 22:57
Answer is A
Reasoning
For any set of numbers in AP, sd is given by difference*[(n^2-1)/12]
Here difference is 2 (even numbers)
we just need n to find sd.

Option A alone is sufficient.
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What is the Standard Deviation of a set of consecutive even integers ?   [#permalink] 12 Jan 2019, 22:57
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