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Water Tank

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by singhsa » Tue Sep 14, 2010 11:08 am
Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end?

a. For each tank, 30% of water at the beginning was removed
b. The average volume of water in the tanks at the end was 63 gallons

OAa
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Source: — Data Sufficiency |
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by GMAT Hacker » Thu Sep 23, 2010 5:45 am
singhsa wrote:Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end?

a. For each tank, 30% of water at the beginning was removed
b. The average volume of water in the tanks at the end was 63 gallons

OAa

Could you please tell what is your doubt so that we can try to help you?
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by this_time_i_will » Thu Sep 23, 2010 9:31 am
A. Stmt I is sufficeint, as the std. deviation wud not change.
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by gmatmachoman » Thu Sep 23, 2010 9:36 am
singhsa wrote:Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end?

a. For each tank, 30% of water at the beginning was removed
b. The average volume of water in the tanks at the end was 63 gallons

OAa
This one really test the fundae of SD

Rule :When the relative change in entities in a list is SAME , then SD remain SAME

St1 :For each tank, 30% of water at the beginning was removed

As per the rule , SD is same as 10 units

Sufficient

St 2 :The average volume of water in the tanks at the end was 63 gallons

For this, we need to initial quanitity & the quantity removed to cal. the new SD
Insufficient

Pick A
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by Ian Stewart » Thu Sep 23, 2010 9:48 am
gmatmachoman wrote: This one really test the fundae of SD

Rule :When the relative change in entities in a list is SAME , then SD remain SAME

St1 :For each tank, 30% of water at the beginning was removed

As per the rule , SD is same as 10 units

Sufficient
No, this is not the case. If you reduce all of the quantities by 30%, *all* of the distances between quantities go down, by exactly 30%. So the standard deviation will *not* stay the same; it will drop by 30%. The answer is still A, because if we know the initial standard deviation is 10, we know the new standard deviation will be 7.

You might be thinking of a situation where we simply *add* or *subtract* a number from everything in a set. Here, if we simply removed 1 gallon of water from each tank, then all of the distances in our set would remain unchanged. Then the standard deviation would not change at all; it would still be 10. But if we *multiply* each element in our set by a constant, as in this question (we are multiplying by 0.7), we are changing all of the distances in the set, and this will certainly change the standard deviation.
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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by GMATMadeEasy » Fri Sep 24, 2010 7:06 am
so logical extrnsion of this is the rule that if all values are multiplied or divided by a constant number, resultant SD is also multiplication or division of previous SD by the same constant ?
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by GMATMadeEasy » Fri Sep 24, 2010 7:07 am
and of course, if it a negative constant, negative sign has no effect on the value .
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