M7MBA wrote:A data set consists of three integers. What is the standard deviation of this data set?
(1) The average (arithmetic mean) and the median are both 3
(2) At least two of the numbers are 3.
Target question: What is the standard deviation of the 3-integer data set?
Statement 1: The average (arithmetic mean) and the median are both 3
Let's TEST some values.
There are several sets that satisfy statement 1. Here are two:
Case a: {3, 3, 3}. Notice that the median and mean both equal 3. In this case, the
standard deviation is 0
Case b: {1, 3, 5}. Notice that the median and mean both equal 3. In this case, the
standard deviation is NOT 0
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: At least two of the numbers are 3
There are several sets that satisfy statement 1. Here are two:
Case a: {3, 3, 3}. In this case, the
standard deviation is 0
Case b: {3, 3, 100}. In this case, the
standard deviation is NOT 0
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that the average (arithmetic mean) and the median are both 3. This means
the 3 numbers MUST ADD to 9
Statement 2 tells us that at least two of the numbers are 3.
If two of the numbers are 3's AND all three numbers must add to 9, then all three numbers MUST be 3's
That is, the set MUST be {3, 3, 3}, in which case, the
standard deviation is 0
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
