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standard deviation-very deviating infact

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by clammiestqasar » Sat Oct 09, 2010 10:09 pm
70,75,80,85,90,105,105,130,130,130

The list shown consists of the times in seconds that it took each of 10 school children to run a distance of 400 m.If the standard deviation of the 10 running times is 22.4 seconds,how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
1
2
3
4
5

mean - 100
1 SD below the mean = 77.8
thus there are 5 times above
But OA is 2
Please help?
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by limestone » Sat Oct 09, 2010 10:56 pm
clammiestqasar wrote:70,75,80,85,90,105,105,130,130,130

The list shown consists of the times in seconds that it took each of 10 school children to run a distance of 400 m.If the standard deviation of the 10 running times is 22.4 seconds,how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
1
2
3
4
5

mean - 100
1 SD below the mean = 77.8
thus there are 5 times above
But OA is 2
Please help?
Hi,
I guess your problem is here:

X is more than 1 standard deviation below the mean
Y is 1 standard deviation below the mean

So X and Y, which is greater?

mean - X = more than 1 SD
mean - Y = 1 SD

Then Y> X

In the above question Y = 77.8
Then X can only be 70,75.

Thus 2 is the answer.[/quote]
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
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by uwhusky » Sat Oct 09, 2010 11:04 pm
On a minor side note, 100 - 22.4 = 77.6, not 77.8.

Any number below 77.6 is at least 1 deviation below the mean.

I do not understand what you meant by "there are 5 times above."
Yep.
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by clammiestqasar » Sat Oct 09, 2010 11:34 pm
q says how many of the times are MORE than one SD below the mean?
1 SD below the mean is 77.6
Now whatever times are more than 77.6 will fall in this category?

I am sorry but i couldnt understand the above stated explanation
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by uwhusky » Sat Oct 09, 2010 11:53 pm
Oh...I get where the confusion is.

The question asked: "how many of the 10 running times..."

That means how many numbers out of the 10 numbers listed are at least 1 standard deviation below the mean.
Yep.
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by clammiestqasar » Sat Oct 09, 2010 11:59 pm
i got that man.The q says how many numbers are more than 1 standard deviation less than the mean that means how many nos are more than 77.6 and not less??
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by uwhusky » Sun Oct 10, 2010 12:05 am
How did you get "more" instead of "less"?

I think I get it...

You're confused with "more than 1 standard deviation" and "below the mean" combined in one sentence.

Maybe you should read through MGMAT Word Translation book about standard deviation before proceeding. I don't think you fully understand the concept of standard deviation, and thus you're struggling with this question.
Last edited by uwhusky on Sun Oct 10, 2010 12:11 am, edited 2 times in total.
Yep.
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by clammiestqasar » Sun Oct 10, 2010 12:07 am
just read the q once more .It says how many nos are more and not less?that is what i am confused about .
Its a gmat prep q.
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by uwhusky » Sun Oct 10, 2010 12:12 am
Calm down, it's YOU who are struggling with understanding the question, not me. I am trying to help you and you're frustrated because I cannot understand your lack of ability to articulate your confusion?
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by clammiestqasar » Sun Oct 10, 2010 12:18 am
No,i am frustrated because I cannot understand the q.According to the answer and everyone's suggestions I know what you are trying to say. But my brain just wouldnt accept and i dont know why.I am sorry if i expressed any sort of unwanted reaction.
It still reads that the question wants how many numbers are more than 1 SD less than the mean.
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by uwhusky » Sun Oct 10, 2010 12:23 am
Mean = 100.

1 SD below mean = 77.6.

1 SD above mean = 122.4.

2 SD below mean = 55.2

2 SD above mean = 144.8.

So the question asks, "how many of the 10 running times are more than 1 standard deviation below the mean..."

Anything below 77.6 fits the criterion. If the question asks how many are more than 2 standard deviation below the mean, then anything below 55.2 fits that criterion.

If you still don't get the question, maybe you should try come back to it tomorrow or another day. It helps to give your brain a break.
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by clammiestqasar » Sun Oct 10, 2010 1:42 am
I do.Thanks a lot =)
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