Problem Solving

I found this in a practice test and I selected 3 as I took below the mean meaning slower than the mean which means bigger numbers than the mean. The answer is actually 2 as that is the amount of people who ran a time which is below the mean (a faster time so a smaller number). Does it seem wrong?

70,75,80,85,90,105,105,130,130,130

The list consists of times (in seconds) it took people to run a distance of 400m. If the standard deviation of the 10 running times is 22.4 seconds (rounded up to one tenth of a second) from the mean, how many of the 10 running times are more than 1 standard deviation from the mean?

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5

Lookingfor700GMAT wrote:I found this in a practice test and I selected 3 as I took below the mean meaning slower than the mean which means bigger numbers than the mean. The answer is actually 2 as that is the amount of people who ran a time which is below the mean (a faster time so a smaller number). Does it seem wrong?

70,75,80,85,90,105,105,130,130,130

The list consists of times (in seconds) it took people to run a distance of 400m. If the standard deviation of the 10 running times is 22.4 seconds (rounded up to one tenth of a second) from the mean, how many of the 10 running times are more than 1 standard deviation from the mean?

1
2
3
4
5

IMO B
more than 1 standard deviation from the mean---------->100-22.4=77.6

so all the values > or < than 77.6 is one sd from mean
here two values are less than 77.6
and 8 values are >77.6
but since option does not contain 8 so 2 is the ans

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!

IMO E


ie 5

Lookingfor700GMAT wrote:I found this in a practice test and I selected 3 as I took below the mean meaning slower than the mean which means bigger numbers than the mean. The answer is actually 2 as that is the amount of people who ran a time which is below the mean (a faster time so a smaller number). Does it seem wrong?

70,75,80,85,90,105,105,130,130,130

The list consists of times (in seconds) it took people to run a distance of 400m. If the standard deviation of the 10 running times is 22.4 seconds (rounded up to one tenth of a second) from the mean, how many of the 10 running times are more than 1 standard deviation from the mean?

1
2
3
4
5

Data with SD 22.4 is present. Quickly get the AM as 100. More than 1 standard deviation from the mean on both sides are the data that are either less than 100 - 22.4 (< 77.6), or more than 100 + 22.4 (> 122.4).

Why just 2? Anybody?

The answer is obviously 5 - no idea where 2 has come from

Thanks to yeahdisk, sanju09, and girish3131 for the correct answer. I assumed that in the original post we were given the correct answer and only focused on "how" to get there using a simpler example. A quick check of the mean (and it is 100) means that the range within one standard deviation is as sanju09 tells us 77.6 to 122.4 and there are five values outside of that range.

I have corrected my explanation above to include the correct answer.

Thanks guys!