Is the standard deviation of numbers w,x,y and z greater than 2?
2) The average of the four numbers is 8
You might be able to see intuitively why the answer should be C here - if the average of our four-element set is 8, and one of the elements is equal to 3, then at least one of our elements is pretty far from the mean. That's certainly going to guarantee something
about our standard deviation - the standard deviation can't be all that small here.
You can prove that the answer is C, at least if you remember how you find the standard deviation (not something you ever need to calculate on the GMAT, incidentally) - you find the distance from each element to the mean, square those distances, average these squares, then finally take the square root. If our mean is 8, and one of our elements is 3, then one of our distances to the mean is 5. So when we add the squares of the distances, our sum must be at least 5^2 = 25. We now take the average of this sum (so here divide by 4); this average is at least 25/4 = 6.25, and the square root of that is greater than 2.
So if we use both statements, the standard deviation must be greater than 2, and the answer is C.
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