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Set P has n integers. What is the standard deviation of Set P?

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Source: — Data Sufficiency |

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Re: Set P has n integers. What is the standard deviation of Set P?

by Brent@GMATPrepNow » Thu Apr 23, 2020 7:45 am

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BTGmoderatorDC wrote: ↑
Wed Apr 22, 2020 6:45 pm
 Set P has n integers. What is the standard deviation of Set P?

(1) The range of Set P is equal to zero
(2) The mean of Set P is equal to the median of Set P
OA A

Source: e-GMAT
Given: Set P has n integers.

Target question: What is the standard deviation of Set P?

Statement 1: The range of Set P is equal to zero
If the range is ZERO then every element in set P must be the SAME.
If all of the values are the same then there is NO DEVIATION, which means the standard deviation of Set P is zero
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The mean of Set P is equal to the median of Set P
There are several scenarios that satisfy statement 2. Here are two:
Case a: Set P = {1,1,1}. Since all the values are the SAME , the standard deviation is 0
Case b: Set P = {1,2,3}. Since the values are DIFFERENT, the standard deviation is NOT 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Re: Set P has n integers. What is the standard deviation of Set P?

by Scott@TargetTestPrep » Sat Apr 25, 2020 1:45 pm

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BTGmoderatorDC wrote: ↑
Wed Apr 22, 2020 6:45 pm
 Set P has n integers. What is the standard deviation of Set P?

I. The range of Set P is equal to zero

II. The mean of Set P is equal to the median of Set P


OA A

Source: e-GMAT
Solution:

We need to determine the standard deviation of set P.

Statement One Alone:

The range of Set P is equal to zero

Since the range of set P is zero, all the integers in set P are the same. Thus, the standard deviation is zero. Statement one alone is sufficient.

Statement Two Alone:

The mean of Set P is equal to the median of Set P

We could have Set P = {5, 5, 5, 5, 5, } or {1, 1, 5, 9, 9}. Although the mean and median both equal 5 in each set, the standard deviation of the first example is 0, and the standard deviation of the second example is greater than 0. Thus, we cannot determine a unique value for the standard deviation of Set P. Statement two alone is not sufficient.

Answer: A

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