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Set P has n integers. What is the standard deviation of Set P? 16 May 2019, 00:53
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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
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Set P has n integers. What is the standard deviation of Set P? 16 May 2019, 05:43
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1. Range 0 means all integers are same , so SD is 0

Sufficient

2. Mean =median

Here we can use example to show that is not sufficient

Ex1: 1 2 3
Ex2: 1 5 9

SD is not constant so this is insufficient

:- please lete know if this approach is wrong , just Guessing

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Set P has n integers. What is the standard deviation of Set P? Updated on: 17 May 2021, 08:31
Originally posted by BrentGMATPrepNow on 05 Dec 2019, 10:38.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:31, edited 1 time in total.
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kiran120680
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
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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

Cheers,
Brent

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Set P has n integers. What is the standard deviation of Set P? 30 Apr 2020, 03:41
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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
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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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Set P has n integers. What is the standard deviation of Set P? 30 Apr 2020, 09:37
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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
Show more

126Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Condition 1) is sufficient for the following reason.
The five statements are equivalent each other.
1. The standard deviation of P is 0.
2. All data of P are equal.
3. The range of P is 0
4. The maximum of P is equal to the average of P.
5. The minimum of P is equal to the average of P.
Since condition 1) is the case 3, P has the standard deviation 0.

Condition 2)
{1,2,3} and {2,4,6} have different standard deviations, even thought each of them has its average equal to it median, respectively.
Since it does not yield a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
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Set P has n integers. What is the standard deviation of Set P? 28 Mar 2024, 08:02
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