Mean, Standard Deviation - MGMAT cat question

Generally speaking, "within one standard deviation from the mean" means number Greater OR Smaller than the mean - one SD up or down from the mean. In the above example, numbers within one SD from the mean fall within the range of 60+/- 3.5 = numbers between 56.5 and 63.5.

Here, since you want the smallest number that falls within the range, I'll have to go with C 59 - since 56 is "more than one STD away from the mean", it falls outside of the range, leaving 59 the smallest number (among the choices presented) that is still within the range.

rishikeshranga 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?

53

56

59

63.5

65

This is a very poorly worded question; technically, the smallest number that falls within one standard deviation of the mean is 56.50000000000000....00001, which isn't among the choices, leaving you with no correct answer. You will never see a question worded this way on the actual GMAT - what's the source?

The flaws aside, however, this is a style of question that's been appearing on the GMAT of late and which is extremely simple to answer once you understand it.

To solve this style of question, simply draw a number line with the mean in the middle:

-----------------60-----------------

Next, plot points on the number line based on the given standard deviation. Since in this case the SD is 3.5, we'll plot points 3.5 away from the mean in each direction:

----------56.5------------60-----------63.5---------------

This question only asks about results within 1 SD of the mean, so we don't need to go any further - we know the answer has to be between 56.5 and 63.5. If the question had been "which of the following results is between 1 and 2 SDs from the mean?", we'd have plotted 1 step further in each direction:

---------53----------56.5----------60----------63.5-----------67---------

and chosen an answer between 53 and 56.5 OR between 63.5 and 67.

As Geva notes, it's important to read the question carefully; sometimes we're asked for a number a certain distance below the mean, sometimes above the mean, sometimes within a certain range of the mean and sometimes a specific distance away from the mean.

This question is asked in MGMAT's one of the online CAT exams

Thank you for your replies..

It really helped clarify my doubts and understanding about the standard deviation..

I believe that the wording is absolutely okay here. It says "which OF THE FOLLOWING is the smallest number...".

59 IS indeed the smallest number among the answer choices (which apparently are meant by "of the following") that fulfills the mentioned requirement.

Standard deviation=distance from mean

Mean =60

S.D= 3.5

The values within 1 standard deviation range from 56.5<x<63.5.where x is that number.

63.5 is not within 1 S.D .It infact is exactly 1 S.D from 60.

59 should be the answer because it satisfies the condition 56.5<x<63.5 and also because it is the smallest one.