BTGModeratorVI wrote: ↑Sun Apr 05, 2020 9:04 am
If the average (arithmetic mean) of a, b and c is m, is their standard deviation less than 1?
1) a, b and c are consecutive integers with a < b < c.
2) m = 2
Answer:
A
Source: Math Revolution
Target question: Is the standard deviation of a, b and c less than 1?
Statement 1: a, b and c are consecutive integers with a < b < c.
It's important to know that standard deviation is a measure of dispersion (how spread apart the values are).
So, ANY 3 consecutive integers will have the same standard deviation.
For example, the standard deviation of {1,2,3} = the standard deviation of {6,7,8} = the standard deviation of {23,24,25} etc
So, IF we calculate the standard deviation of {1,2,3} then THAT value will provide sufficient info to the answer to the
target question
Since we COULD answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: m = 2
There are several values a, b and c that satisfy statement 2. Here are two:
Case a: a = 2, b = 2 and c = 2 (mean = 2 and standard deviation = 0). In this case, the answer to the target question is
YES, the standard deviation IS less than 1
Case b: a = -100, b = 0 and c = 106 (mean = 2 and standard deviation = some number much greater than 1. In this case, the answer to the target question is
NO, the standard deviation is NOT less than 1
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
