One of the various ways that they test standard deviation on the GMAT - and the one that I have seen the most in official questions - is what you have listed here, namely they give you a set of numbers and the standard deviation and you are asked to apply it...this is much more straight-forward than having to calculate the deviation yourself!
The first thing you need to know about standard deviation is that it is both above and below the mean. The "deviation" can be either higher or lower - the word "more" does not apply to the times of the runners - as in faster OR slower - but "more" applies to the distance from the mean. Let's look at a simpler example.
"The set of weights of five dogs: 30, 35, 40, 45, 50.
The standard deviation is 6.2" (this will always be given to you in the problem).
"How many weights are more than one standard deviation from the mean?"
The first thing you must do is to calculate the mean. In my simpler example, because of the even distribution the median is the mean so the mean (or average) is the middle number (or median) = 40. In most cases - as in your problem above you will need to calculate the mean by adding together all of the numbers and dividing by the number of entries, so 30+35+40+45+50 = 200/5 = 40. The mean is the bit of information they do not supply and that you must calculate.
Next, you simply apply the standard deviation that they have supplied for you in the question. In this case that is 6.2. Remember that you must go both directions above AND below the mean. (A bird needs two wings of equally length to fly and so does standard deviation!) So add 6.2 (S.D.) to 40 (the mean) = 46.2 AND also subtract 6.2 from 40 = 33.8. This means that all values within the range 33.8 to 46.2 are within one standard deviation from the mean. Now you simply identify the values that fall outside of this range. In this case 30 on the extreme low side of the set and 50 on the extreme high side are the two values that fall outside of this range.
In the case of your problem above, you just need to calculate the mean and apply the given deviation of 22.4. I think you will find exactly five values are more than one standard deviation from the mean!
Good problem!
Last edited by
David@VeritasPrep on Sat Mar 13, 2010 5:30 am, edited 1 time in total.
