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standard deviation of Set Y

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by j_shreyans » Mon Oct 27, 2014 11:51 am
If the standard deviation of Set Y is 4, what are the greatest and least values that are within one standard deviation of the mean?

(1) The median of Set Y is 5.

(2) The mean of Set Y is 6.
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Source: — Data Sufficiency |

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by [email protected] » Mon Oct 27, 2014 10:44 pm
Hi j_shreyans,

When a question asks about values that are within a certain number of standard deviations away from a mean, you need to know two things:
1) The standard deviation
2) The mean

In this prompt, we're given the standard deviation (in this case, 4), so we need the mean to figure out what values are within 1 SD of the mean.

Fact 1: The median = 5

This is NOT the mean, so we have no way of answering the question.
Fact 1 is INSUFFICIENT

Fact 2: The mean = 6

This IS the mean, so we CAN answer the question. since the SD is 4, the values within 1 SD of the mean are 2 to 10, inclusive.
Fact 2 is SUFFICIENT

Final Answer: B

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by GMATGuruNY » Tue Oct 28, 2014 1:51 am
j_shreyans wrote:If the standard deviation of Set Y is 4, what are the greatest and least values that are within one standard deviation of the mean?

(1) The median of Set Y is 5.

(2) The mean of Set Y is 6.
Let m = the mean of Set Y.
Since the SD (standard deviation) of Set Y = 4, we get:
One SD below the mean = m-4.
One SD above the mean = m+4.
Thus:
Any value between m-4 and m+4, inclusive, is within one SD of the mean.

The question stem asks for the values of m-4 and m+4.
To determine these values, we need to know the mean of Set Y.
Question stem, rephrased:
What is the mean of Set Y?

Statement 1: The median of Set Y is 5
INSUFFICIENT.

Statement 2: The mean of Set Y is 6
SUFFICIENT.

The correct answer is B.
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