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February 22nd, 2012, 11:35 AM   #1
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Help!-Variance and Standard Deviation

Okay, I have a word problem here:

Seven Students recorded the marks which they obtained in an intelligence test. Their mean mark was 65 and their standard deviation 10. An eighth student obtained a mark of 65. Calculate the mean and standard deviation of the marks of all eight students.

I understand how they get the mean, because it's just [(65*7)+65]/8, which gives you 65- easy enough.

But for the standard deviation I keep getting zero! The answer is supposed to be 9.4, could someone please show me how this answer is obtained? I'm clueless!

Many thanks in advance!
margybear is offline  
 
February 22nd, 2012, 12:06 PM   #2
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Re: Help!-Variance and Standard Deviation

Sup bro

The way I calculate SD is by subtracting the differences of the mean (65) from each of the grades (unknown), then squaring those differences and adding those squares up, then dividing that number by the number of grades minus one (initially 6 in your case before adding the 8th student), then taking the square root of that number.

So let's reverse engineer the final SD as far back as we can.

You stated the SD was 10, so let's square that because we're going backwards and 10 was the square root of 100, and 100 was the sum of the squared differences divided by the number of students.

So now you have 100, and you want to multiply that by 6 because you divided it by 6 (one less than seven students) in the first place to get the SD of the 7 students.

So now you have 600, which was the sum of the squared differences of the grades.

You can't go further here because you need the square roots of each difference in grades, but you don't have access to that information, but no worries, you don't need to

The deviation of the 8th student is the mean grade subtracted from the student's grade, so we get 0 anyway (65-65 obviously).

So it's still going to be 600 since there's no calculation to make for this student's grade. The number of students just got upped 1.

Alright, let's move forward again, instead of backwards.

You have 600 + 0 which is 600, and now you just have to divide that by the number of total students (now 8 students) minus one, so that's 600 / 7.

So you have the fraction 600/7 which you can't simplify, and just take the square root of that for the final SD answer, which if you perform on a calculator will be roughly about 9.26

There's probably a whole formula and stuff but I don't remember all of it so this is just the easy way. Maybe someone more skilled can post the more advanced formulaic method, sorry
daigo is offline  
February 22nd, 2012, 12:08 PM   #3
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Re: Help!-Variance and Standard Deviation

Ahh, thank you so much!
It makes a lot more sense now, thanks!
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February 22nd, 2012, 10:10 PM   #4
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Re: Help!-Variance and Standard Deviation

Quote:
Originally Posted by daigo
Sup bro
Hmm <noting name and picture>


Quote:
There's probably a whole formula and stuff but I don't remember all of it so this is just the easy way. Maybe someone more skilled can post the more advanced formulaic method, sorry
I don't think there is any special equation for it. I used the same method you did, just simply recognizing that the new student being 65 was adding nothing to our total, and I would guess that was the whole point of the problem.
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