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Fri Jan 31, 2020 5:54 am

Economist GMAT

What is the standard deviation of a set of numbers whose mean is 20?

1) The absolute value of the difference of each number in the set from the mean is equal.
2) The sum of the squares of the differences from the mean is greater than 100.

OA E

Let's take each statement one by one.

1) The absolute value of the difference of each number in the set from the mean is equal.

Case 1: Say the numbers are 10 and 30. Mean = 20. We see that |10 – 20| = |30 – 20|. Note that computation of standard deviation (SD) is beyond the scope of the GMAT; however, its analysis and interpretation are.

SD will be determined by 10 and 30. Let's hold here.

Case 2: Say the numbers are 100 and 300. Mean = 200. We see that |100 – 200| = |300 – 200|.

Since the deviations of 100 and 300 from their mean (200) are far greater than the deviations of 10 and 30 from their mean (20), SD for Case 2 will be greater than that for Case 1. The value of SD will be different. Insufficient.

2) The sum of the squares of the differences from the mean is greater than 100.

Certainly insufficient.

(1) and (2) together

Even both statements together can't help us determine the value of SD> Insufficient.

The correct answer: E

Hope this helps!

-Jay
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