rishianand7 wrote:Set T consists of a certain number of even integers divisible by 3. Is standard deviation of set T positive?
(1) All elements of set T are positive.
(2) The range of set T is 0
Target question: Is standard deviation of set T positive?
IMPORTANT: The standard deviation of any set is always greater than or equal to zero. So, either the standard deviation is zero or it's positive. The standard deviation will EQUAL ZERO if all of the numbers in the set are IDENTICAL. The standard deviation will BE POSITIVE if the numbers in the set are
NOT IDENTICAL.
Statement 1: All elements of set T are positive
There are various sets of numbers that meet this condition. Here are two:
Case a: the numbers are {6, 12, 18}. Since the numbers are not all identical,
the standard deviation is positive
Case b: the numbers are {6, 6, 6}. Since the numbers are identical, the standard deviation is zero. In other words,
the standard deviation is not positive
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The range of set T is 0
If the range = 0, then the numbers (or number) in the set are IDENTICAL, which means the standard deviation is zero.
In other words,
the standard deviation is definitely not positive
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
