standard deviation (gmat prep q)

karenmeow · Posted: Sat Jul 19, 2008 10:18 am Post subject: standard deviation (gmat prep q)

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

answer: 3

pepeprepa · Posted: Sat Jul 19, 2008 10:51 am Post subject:

Sum of all times: 1000
Mean of the 10 running times=100
1 standard deviation is 22.4 seconds, so the question asks you how many runners have a time which is superior to 122.4 seconds.
There are three times above (the three 130).

louvre · Posted: Wed Jul 23, 2008 5:49 am Post subject:

pepeprepa · Posted: Wed Jul 23, 2008 6:56 am Post subject:

Sorry for this concentration error, you are right.
We have 2 now

AleksandrM · Posted: Wed Jul 23, 2008 9:25 am Post subject:

My answer is also 2. The times sum to 1000 w/ a mean of 100

100 - 22.4 = 77.6 anything below that is more than 1 standard deviation below the mean.

mehravikas · Posted: Mon Aug 25, 2008 4:04 pm Post subject:

"how many of the 10 running times are more than 1 standard deviation below the mean"

Mean = 100, Standard Deviation = 22.4
1 standard deviation could be = 100 - 22.4 = 77.6 or 100 + 22.4 = 122.4
now the other part asks for more than 1 standard deviation - the items would be 80, 85, and 90. (more than 77.6)

other standard deviation 122.4 - items more than standard deviation - 130, 130, 130

answer would be 3 because 130 is more than the mean and 80, 85 and 90 are less than the mean but more than the standard deviation.

Hope this is clear.

anju · Posted: Tue Aug 26, 2008 8:21 am Post subject:

mehravikas · Posted: Tue Aug 26, 2008 11:00 am Post subject:

Sorry anju but I am not convinced. Can we have the official answer please?

parallel_chase · Posted: Tue Aug 26, 2008 11:36 am Post subject:

The answer is 2.

Are more than 1 standard deviation below the mean of the 10 running times.

This mean what is number of running time are below 1st SD below the mean.

mean =100
1SD below the mean = 77.6

number of running times < 77.6

75, and 70.

Hope this helps.

mehravikas · Posted: Tue Aug 26, 2008 11:48 am Post subject:

If the answer is 2.

Then I think there is a problem in the way question is phrased. "more than 1 standard deviation below the mean"