BTGModeratorVI wrote: ↑Wed Jan 06, 2021 8:08 am
The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?
(A) 38 to 46
(B) 38 to 54
(C) 42 to 50
(D) 44 to 48
(E) 46 to 50
Answer:
B
Source: Princeton Review
-----------ASIDE-----------------
A little extra background on
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.
----------------------------------
The arithmetic mean of a data set is 46 and the standard deviation of the set is 4. Which of the following contains the interval two standard deviations from the mean of the set?
2 standard deviations ABOVE the mean = 46 + 2(4) =
54
2 standard deviations BELOW the mean = 46 - 2(4) =
38
The range =
38 to
54
Answer: B
Cheers,
Brent
