HarveyS 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

-----------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 to 63.5So, 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

_________________

Brent Hanneson – GMATPrepNow.com

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