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I got this below question as my first quant question in GMT prep 2. Please help me with the solution.
A certain list of 100 data has an average of 6 and standard deviation of d where d is positive. Which of the followig pairs of data, when added to the list must result in a ist of 102 data with the standard deviation less than d?
Answer choices -
1. 0 and 6 2. 0 and 12 3. 0 and 0 4. -6 and 0 5. 6 and 6
Standard deviation, by definition is a measure of the variability or dispersion of a population, a data set, or a probability distribution.
Once all the options have two numbers, each one of them, when added, will result in a list of 102 elements. So the point is how to make the standard deviation lower.
According to the definition if you add numbers farther then the average this makes the standard deviation grow. In the same way, the closer the new numbers are of the average, the lower will be the standard deviation.
Thus, E is the answer, since both values are equal to the average.
I did GMATPrep 2 yesterday, and faced this as the first question,too. I was really nervous and excited because I never imagined that a S.D. problem would come up the first one. However, GMAT always make us surprised.
Just curious - to switch this question around, which set of numbers, when added to the list, would result in the largest standard deviation from d?
Would it be 0 and 12?
now SD will be maximum if we have 2 numbers with maximum difference from avg. If we take 0 and 12 we get to add 2*6^2. But ifwe consider 0 and -6 we get to add 6^2 + 12^2 which will give the largest SD
Re: Standard deviation question
14 Oct 2009, 14:46