sana.noor wrote:Given that the mean of Set A is 10, what is the range of two standard deviations above and below the mean?
(1) One standard deviation above and below the mean ranges from 7 to 13.
(2) The median of set A is 11.
A little background on "
two standard deviations above and below the mean"
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations above the mean = 17
[since 9 + 2(4) = 17]
1.5 standard deviations below the mean = 3
[since 9 - 1.5(4) = 3]
3 standard deviations above the mean = 21
[since 9 + 3(4) = 21]
etc.
Now, onto the question.
Target question: What is the range of two standard deviations above and below the mean?
Given: The mean is
10
Statement 1: One standard deviation above and below the mean ranges from 7 to 13.
So, mean - (1 standard deviation) = 7, and mean + (1 standard deviation) = 13
The mean is
10, so
10 - (1 standard deviation) = 7, and
10 + (1 standard deviation) = 13
So, we can conclude that 1 standard deviation = 3
From here, we know that 2 standard deviations = 6
2 standard deviations below the mean =
10 - 6 =
4
2 standard deviations above the mean =
10 + 6 =
16
The range from 4 to 16 = 12
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The median of set A is 11
This tells us nothing about the standard deviation of set A.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
