The reasoning for the answer being E is not b/c the difference between the added data points and the mean is the least possible. Clearly the difference between -6 and 6 (-6-6=-12 <6-6=0) is smaller. The key is in the calculation of standard deviation,THESE DIFFERENCES ARE SQUARED so that the least becomes the greatest IF THE LEAST IS NEGATIVE!!. (-12)^2 >0^2. If the answer choice did not have a negative data point, your reasoning would have been valid, since O, which is neither positive nor negative is the least of all positive numbers squared. See this as a CR exercise which though you reasoned wrongly you still got right. (laugh),manoj0609 wrote:Definetly the ans should be E .
SD is more when the difference between mean and a datapoint is large
and viceversa.
here we have to reduce the SD which means need to include datapoints in such a way that difference is as low as possible. if we add 6 and 6 the diff betn mean and these poitns is zero i.e least possible and hence this can give u least SD among all the options.
Cheers,manu
Original Datamanoj0609 wrote:Could you please elaborate more on this? I am not quite convinced with your reasoning.
manu's reasoning above was perfectly valid. Perhaps it would be more clear to say 'positive difference', or 'distance', rather than simply 'difference', but the logic was otherwise fine.dtweah wrote: The reasoning for the answer being E is not b/c the difference between the added data points and the mean is the least possible.
Not sure how you got 1.632 here. The standard deviation of {-1, 1, 1} is:dtweah wrote:
SD:( ((1- 1/3)^2 +(1- 1/3)^2) + (-1-1/3)^2)/3)^.5
Now the point I am making can be seen in the third parenthesis above. -1-1/3 is the least of corresponding expressions without squaring them. But you cannot say so when we square them.
((2/3)^2 + (2/3)^2 + (4/3)^2)/3)^.5
(4/3)^2 > (2/3)^2
SD in this case = 1.632
Ian Stewart wrote:manu's reasoning above was perfectly valid. Perhaps it would be more clear to say 'positive difference', or 'distance', rather than simply 'difference', but the logic was otherwise fine.dtweah wrote: The reasoning for the answer being E is not b/c the difference between the added data points and the mean is the least possible.
In general, when thinking about standard deviation, you should think in terms of distances to the mean, and not differences from the mean; otherwise you might be distracted by negative signs that aren't at all important. That is, if you're looking at this set: {1, 2, 3, 4, 5}, if you calculate the difference ("mean - x") for each x in the set, some of these differences will be positive, some negative. Those negative signs aren't important, since standard deviation is only based on distances from each element to the average - you can feed the numbers 2, 1, 0, 1, 2 into the standard deviation calculation to get the correct answer. Mind you, I've yet to see a real GMAT question that requires you to calculate standard deviation.
Since as you say those negative signs are not important, that is why the concept of Least is problematic, which is what I pointed out to him. If we squared the terms, the negative signs vanish so not important at all. Anyway the discussion was good b/c it helped reinforced concepts which may be needed on some Future SD problems. I agree they wouldn't ask u to calculate SD but if these principals are known, one can save a lot of time over some simple problems that appear difficult.
