vaibhav101 wrote:if a set consists of a certain number of even integers divisible by 3 , is the standard deviation of the set positive?
1) all elements of set are positive
2) the range of set is 0.
Target question: Is the standard deviation of the set positive?
KEY CONCEPT: If all of the numbers in a set are EQUAL, then the standard deviation = 0
If the numbers in a set are NOT all equal, then the standard deviation > 0
Given: The set consists of a certain number of even integers divisible by 3
Statement 1: All elements of set are positive
There are several sets of numbers that satisfy statement 1. Here are two:
Case a: The set is {6, 6, 6, 6, 6}. In this case, the standard deviation is ZERO, which means the answer to the target question is
NO, the standard deviation is NOT positive
Case b: The set is {6, 12, 36}. In this case, the answer to the target question is
YES, the standard deviation IS positive
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The range of set is 0
If the range = 0, then all values in the set are EQUAL
This means the standard deviation is ZERO, which means the answer to the target question is
NO, the standard deviation is NOT positive
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
