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Sets Question

by prashanthichennupati » Sun Jul 21, 2013 7:31 pm
Set A consists of five different numbers; set B consists of four different numbers, each of which is in set A. Is the standard deviation of set A less than the standard deviation of set B ?

(1) Set A contains five consecutive integers.

(2) The average (arithmetic mean) of set A is equal to the average (arithmetic mean) of set B.

Can anyone explain how Option 2 alone is sufficient?

Thanks in Advance
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Source: — Data Sufficiency |

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by [email protected] » Sun Jul 21, 2013 8:18 pm
Hi prashanthichennupati,

Standard Deviation is a rare subject on the GMAT; you'll likely only see it once in the Quant section. Standard Deviation is based on a very specific math formula, that essentially tells you "how spread out" a group of numbers is. If the numbers are far apart, then the SD is bigger; if the numbers are closer together, then the SD is smaller. You don't need to know the formula so much as you need to know the concept.

In this DS question, we're told that all the numbers in Set B are also in Set A AND that Set A has one additional number in it. The question itself asks if the SD of A is < the SD of B? That one extra number will affect the SD of Set A depending on if the number is close to, or far from, the average.

Fact 2 tells us that Set A and Set B have the same average. That means that the extra number in Set A has to match the average of Set B (it's the ONLY way that the two averages would match).

For example:
Set B = 1, 2, 3, 4 Avg. = 2.5
Set A = 1, 2, 3, 4, X Avg. = 2.5 so X must = 2.5

What this all means is that the extra number in Set A shrinks Set A's Standard Deviation by putting in a number that makes the group "closer together". So, Fact 2 is SUFFICIENT to answer the question.

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