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# There is a set of consecutive even integers. What is the

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Re: Example #2 of SD from gmat math book [#permalink]
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Pardon me. Let me try. The sd is a measure of the compactness. The consecutive integers are packed the same way ( equidistant ) from each other no matter where you start counting from. To get the distances from the mean of a data sample you just need the number of elements. Let's say it is 5 and data set is {1 2 3 4 5} the mean is middle number 3. Because of symmetry and knowing data is equidistant from each other, we can calculate the square of individual distances from the mean. Hence we can know the variance. Hence we can get the sd. So here A is sufficient to answer the question. because of symmetry the sd of {1 2 3 4 5} is same as the sd of {96 97 98 99 100} or {11 12 13 14 15} ie any consecutive 5 integers

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Re: Example #2 of SD from gmat math book [#permalink]
To add on top of what gmat1220 has mentioned, assume that you have a set of 39 consecutive even numbers, then the median = mean and thus two numbers on either side of mean will be 2 away, the next two will be 4 away, and so forth. So this gives the number of distances from mean, and the number of terms is already there, so you can substitute and find the SD.( Of course this is a SD question, so no need to calculate any further).

For option 2, there is nothing that gives how the other members of set are placed with respect to mean, or how many numbers are there in the set, and hence there is no definitive answer.

e.g. there could be three members (whereby the SD will be very low), or 100 members, in which case the SD will vary widely as many elements away from the mean will cause the SD to increase.
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Re: Example #2 of SD from gmat math book [#permalink]
thanks a ton guys...ok so statement makes sense, i got that right but my confusion was over statement 2

stmt 2 : it gives us the mean. We already know the that set is set of consecutive even numbers so we know it is evenly distributed so why cant we calculate the SD.

Can someone clarify this.
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Re: Example #2 of SD from gmat math book [#permalink]
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ajit257 wrote:
thanks a ton guys...ok so statement makes sense, i got that right but my confusion was over statement 2

stmt 2 : it gives us the mean. We already know the that set is set of consecutive even numbers so we know it is evenly distributed so why cant we calculate the SD.

Can someone clarify this.

380,382,384. Mean=382. Standard deviation: 2
378,380,382,384,386. Mean=382: Standard deviation: Somewhere between 2 and 4
376,378,380,382,384,386,388; Mean=382: Standard deviation: Somewhere between 4 and 6

Even though the even numbers are symmetrically distributed about the mean, with every inclusion of a pair of numbers, the standard deviation will gradually increase.

380,382,384:
Here there are just two numbers on both sides of 382. The deviation of 380 from the mean 382 is 2; the deviation of 384 from the mean 382 is also 2, thus the standard deviation is 2.

378,380,382,384,386
Here there are 5 numbers.
382 is the mean.
The deviation of 380 from the mean 382 is 2; the deviation of 384 from the mean 382 is also 2;
But,
The deviation of 378 from the mean 382 is 4; the deviation of 384 from the mean 386 is also 4;
Thus the standard deviation will be somewhere between 2 and 4.

Also, as per the rule, the standard deviation increases with increase in the Range of the set.
380,382,384. Range=4
378,380,382,384,386. Range=8
376,378,380,382,384,386,388. Range=12
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Re: Example #2 of SD from gmat math book [#permalink]
so stmt 2 is based on the concept of the more numbers you add closer to the mean ....sd changes.

thanks fluke.
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Re: Example #2 of SD from gmat math book [#permalink]
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fluke wrote:
380,382,384. Mean=382. Standard deviation: 2

Just to clarify, the standard deviation of that set is not equal to 2. If everything in a set is 2 away from the mean, the standard deviation will indeed be 2, but in your example, 382 is not 2 away from the mean; it is equal to the mean. Because of that, the standard deviation will certainly be less than 2.

If you care to complete the calculation, the distances of the elements in the set {380, 382, 384} to the mean are 2, 0 and 2. Squaring these and averaging, we get 8/3, so the standard deviation is sqrt(8/3).
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Re: Example #2 of SD from gmat math book [#permalink]
IanStewart wrote:
fluke wrote:
380,382,384. Mean=382. Standard deviation: 2

Just to clarify, the standard deviation of that set is not equal to 2. If everything in a set is 2 away from the mean, the standard deviation will indeed be 2, but in your example, 382 is not 2 away from the mean; it is equal to the mean. Because of that, the standard deviation will certainly be less than 2.

If you care to complete the calculation, the distances of the elements in the set {380, 382, 384} to the mean are 2, 0 and 2. Squaring these and averaging, we get 8/3, so the standard deviation is sqrt(8/3).

True. My mistake. Thanks.
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Re: There is a set of consecutive even integers. What is the [#permalink]
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Re: There is a set of consecutive even integers. What is the [#permalink]
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