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DS: Standard Deviation

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DS: Standard Deviation

by DCJ » Tue Sep 22, 2009 12:39 pm
What is the standard deviation of Company R's earnings per month for this year?

(1) The standard deviation of Company R's earnings per month in the first half of this year was $2.3 million.

(2) The standard deviation of Company R's earnings per month in the second half of this year was $3.9 million.

Explanation:
Statements (1) and (2) are both insufficient by themselves because they tell us nothing about the data in the other months. We are left with either (C) or (E) as potential answers. Since we know the standard deviation for the two halves of the year, does that mean we can calculate the standard deviation for the whole year? Not necessarily. If the means of the two sets are different, then the mean of the combined set of earnings numbers will have to be calculated, and the standard deviation of the combined set depends on this new mean, which is impossible to determine.

Answer:
The answer, therefore, is (E).

Please Clarify:
So if the mean for each set was the same, how could we calculate the SD for the whole set? Would it just be the average of the SDs for the two sets?
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by sanjib » Tue Sep 22, 2009 2:56 pm
I think it is C
because we can multiply the first half SD with 6 to get the amount
then we can multiply the second half SD also with 6 to get the amount
and then add together both this amount and divide by 6 would provide the SD for the whole year.

how we get six is the bell curve theory of SD
(2+14+34+34+14+2)% total six segment for each curve.
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Re: DS: Standard Deviation

by Ian Stewart » Wed Sep 23, 2009 2:12 am
sanjib wrote:I think it is C
because we can multiply the first half SD with 6 to get the amount
then we can multiply the second half SD also with 6 to get the amount
and then add together both this amount and divide by 6 would provide the SD for the whole year.

how we get six is the bell curve theory of SD
(2+14+34+34+14+2)% total six segment for each curve.
You can't make a bell curve from six points - the normal distribution is an infinite distribution, which is why it's never tested on the GMAT. If you know the 68/95/99.7 'rule' from statistics, it's best to forget it on the GMAT - if you find yourself using it, you're doing something wrong.

DCJ wrote:What is the standard deviation of Company R's earnings per month for this year?

(1) The standard deviation of Company R's earnings per month in the first half of this year was $2.3 million.

(2) The standard deviation of Company R's earnings per month in the second half of this year was $3.9 million.

Please Clarify:
So if the mean for each set was the same, how could we calculate the SD for the whole set? Would it just be the average of the SDs for the two sets?
You won't ever need to know how to do this on the GMAT, but you would not just average the two standard deviations. You actually average the variances of the two sets - recall that the variance is just equal to the square of the standard deviation.

So, if you have two sets that are the same size, and have the same mean, if s and t are the standard deviations of your two sets, then s^2 and t^2 are the variances. If you combine the two sets, the new variance will be the average of the two variances: (s^2 + t^2)/2. The new standard deviation will be the square root of that: sqrt[(s^2 + t^2)/2]. That's not tested on the GMAT though.

That's all based on the means being equal - if the means are different, the variance (and therefore the standard deviation) will be larger than what's given by the formula above.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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