ktrout2020 wrote:A data set with a mean of 60 has a standard deviation of 3.5. Which of the following is the smallest number that falls within one standard deviation of the mean?
A. 53
B. 56
C. 59
D. 63.5
E. 65
Source: Manhattan Prep
-----------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.
-----------ONTO THE QUESTION-----------------------
A data set with a mean of 60 has a standard deviation of 3.5.
So, 1 standard deviation ABOVE the mean =
60 + 3.5 = 63.5
And 1 standard deviation BELOW the mean =
60 - 3.5 = 56.5
Which of the following is the smallest number that falls within one standard deviation of the mean?
The values within one standard deviation of the mean are all values that are
greater than or equal to 56.5 AND
less than or equal t 63.5
So, when we check the answer choices, we see that
59 is the smallest value that fits with the above range of values.
Answer: C
Cheers,
Brent
