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Standard Deviation Question

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by shebinjs » Fri Apr 08, 2011 11:54 pm
Hi Gurus,
I am not sure if this question was already discussed here or not. Can some one pls tell me how to solve the below question?

70,75,80,85,90,105,105,130,130,130
The list shown consists of times, in seconds, that it took each of 10 school children 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?

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by Geva@EconomistGMAT » Sat Apr 09, 2011 1:15 am
shebinjs wrote:Hi Gurus,
I am not sure if this question was already discussed here or not. Can some one pls tell me how to solve the below question?

70,75,80,85,90,105,105,130,130,130
The list shown consists of times, in seconds, that it took each of 10 school children 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?

Thanks.
Find the mean, find how many of the terms above are more than 22.4 seconds below the mean.
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by sanju09 » Sat Apr 09, 2011 1:50 am
shebinjs wrote:Hi Gurus,
I am not sure if this question was already discussed here or not. Can some one pls tell me how to solve the below question?

70,75,80,85,90,105,105,130,130,130
The list shown consists of times, in seconds, that it took each of 10 school children 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?

Thanks.

1 standard deviation below the mean = readings below (mean – 1 SD)

We have SD of 70, 75, 80, 85, 90, 105, 105, 130, 130, and 130 given as 22.4, hence

1 SD = 1 × 22.4 = 22.4

And the mean (AM)

= (70 + 75 + 80 + 85 + 90 + 105 + 105 + 130 + 130 + 130)/10 = 100

All we need to do now is to count how many of the readings above are below 100 – 22.4 = 77.6, and we could count only 2, videlicet 70 and 75.
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by shebinjs » Sat Apr 09, 2011 4:21 am
Hi Sanju,
Thanks for the prompt response. But the questions is "how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?"

So isn't it asking for times greater than 77.6?

I have marked the way I read as bold and underlined above.

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by shebinjs » Sat Apr 09, 2011 4:24 am
Hi Geva,
I did exactly the same thing. So the answer should be the count of times greater than 77.6 (which 1 SD below mean). This gives the answer 8. But the answer choice doesn't have this answer. The answer as per GMAT Prep is 2. I think they might have meant less than (and not more than). So probably a typo in the question??
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by akshatgupta87 » Sat Apr 09, 2011 8:50 am
The question is to calculate the numbers less than mean but greater that 1 SD
See here the mean is 100
so eliminate all numbers above 100
Now, SD=22.4
x1=100-70=30
x2=100-75=25
x3=100-80=20
x4=100-85=15
x5=100-90=10
We are asked about the numbers greater than 1 SD i.e 22.4
therefore x1 and x2 i.e 70 & 75
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by Geva@EconomistGMAT » Sat Apr 09, 2011 8:57 am
shebinjs wrote:Hi Geva,
I did exactly the same thing. So the answer should be the count of times greater than 77.6 (which 1 SD below mean). This gives the answer 8. But the answer choice doesn't have this answer. The answer as per GMAT Prep is 2. I think they might have meant less than (and not more than). So probably a typo in the question??
Ok, I think the problem here is the distinction between "more" and "greater". Your interpretation fits "greater", which means just that - more to the right on the number line. The way the problem is structured, it meas that we're looking for numbers at a distance below the mean that is more than 22.4: all terms smaller than 77.6, of which there are two.
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