Tickle your brain cells: Standard Deviation

[harshitjumma]

I'm struck with this prob.
A set consists of 96 elements. The range of the set is 10 and mean is 12.6. What is the standard deviation?

can we get the exact value of it? or an approximate?

[StaceyKoprince]

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First, note that the GMAT doesn't require you to calculate standard deviation, just to understand what it means. (But maybe that's why you asked whether it could be calculated.)

Second, in order to calculate standard deviation, you do actually need to know the numbers in the set. The mean and the range are not sufficient. Test some real cases to understand why.

Let's say the mean is 12.6 and 94 of the numbers are 12.6 while 2 numbers are 7.6 and 17.6.

That's going to have a different standard deviation than a set in which 48 of the numbers are 7.6 and 48 of the numbers are 17.6. The range is 10, the mean is 12.6... but the SD is different.