Standard deviation below the mean - GMAT PREP

[mehravikas]

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

the list shown consists of times, in seconds, that it took 10 schoolchildren to run a distance of 400 meters. if the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

Answer Choices:
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5
OA: 2
Source GMAT PREP

This question has been posted earlier but the there is still a doubt on the wording of the question.


"more than 1 standard deviation below the mean"?????

[ankitns]

The mean (average) of the 10 running times is 100. 1 std deviation below the mean can be calculated as follows:

Mean - (1 * Standard Deviation)
= 100 - (1 * 22.4)
= 100 - 22.4
= 77.6

Hence the quesiton is asking us to find how many of the 10 running times are below 77.6. By reviewing the list we know that only 2 of these are below 77.6

Hope it helps.

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

the list shown consists of times, in seconds, that it took 10 schoolchildren to run a distance of 400 meters. if the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

Answer Choices:
1
2
3
4
5
OA: 2
Source GMAT PREP

This question has been posted earlier but the there is still a doubt on the wording of the question.


"more than 1 standard deviation below the mean"?????

[DanaJ]

First off, you need to find the mean. It will be easier to calculate if you just consider 70 = a, with 75 = a + 5, 80 = a + 10..., 130 = a + 60.

The sum of the times will be:

a + a + 5 + a + 10 + a + 15 + a + 20 + 2*(a + 35) + 3*(a + 60) = 10a + 50 + 70 + 180 = 10a + 300

The mean will be sum/10 = (10a + 300)/10 = a + 30 = 100. I do believe that using the notation of 70 = a we've spared ourselves a lot of time-munching calculations.

So the mean will be 100. "More than one standard deviation below the mean" means that you are looking for things that are smaller than 100 - 22.4 = 77.6. You get 70 and 75 that qualify, which makes it two times.

If you have "More than one standard deviation above the mean", you are looking for stuff that's greater than 100 + 22.4 = 122.4. You get 130 three times that qualifies.

Hope this helps.

[mehravikas]

Thanks I guess the language is a trap in this question.

I tried numerous calculations and got different answers

First off, you need to find the mean. It will be easier to calculate if you just consider 70 = a, with 75 = a + 5, 80 = a + 10..., 130 = a + 60.

The sum of the times will be:

a + a + 5 + a + 10 + a + 15 + a + 20 + 2*(a + 35) + 3*(a + 60) = 10a + 50 + 70 + 180 = 10a + 300

The mean will be sum/10 = (10a + 300)/10 = a + 30 = 100. I do believe that using the notation of 70 = a we've spared ourselves a lot of time-munching calculations.

So the mean will be 100. "More than one standard deviation below the mean" means that you are looking for things that are smaller than 100 - 22.4 = 77.6. You get 70 and 75 that qualify, which makes it two times.

If you have "More than one standard deviation above the mean", you are looking for stuff that's greater than 100 + 22.4 = 122.4. You get 130 three times that qualifies.

Hope this helps.