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Need maths help
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Old 04 Mar 2010, 01:59   #1 (permalink)
Shas'O
 
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Default Need maths help

Sorry to bother you all, but I can't seem to find the answer in my notes, textbook or on the internets. :P

The problem is this:

Mean <whatever> for a population is X with standard deviation Y in SI units.

What is the mean <whatever> and standard deviation if X & Y are in English units?

I can only guess that there isn't any difference as I'm not given sample size or any other information.

Should it be?

Mean My = aMx
SD = Sy^2 = a^2 Sx^2

Thanks,
Em
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Old 04 Mar 2010, 09:26   #2 (permalink)
Shas'El
 
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Default Re: Need maths help

Quote:
Originally Posted by Emlyn
Mean My = aMx
SD = Sy^2 = a^2 Sx^2
I'm not sure of all the definitions of your terms here, but you look to sort have the right idea.

Just to make everything more explicit:

Let P be a Random Variable with mean X and Standard Deviation Y.
Let Q be a Random Variable of the same data in different units.

Then there will be a linear relationship between Q and P. ie:

Q = aP for some real constant a.

Then, mean(Q) = mean(aP) = a*mean(P) = aX
And SD(Q) = SD(aP) = a*SD(P) = aY

The above results follow by the linearity of the mean and standard deviation.

Note however that the Variance (which is the square of the standard deviation) does not exhibit the same linear behaviour. If you were asked for the variance of Q, rather than the standard deviation, you would get:

Var(Q) = Var(aP) = a[sup]2[/sup]Var(P) = a[sup]2[/sup]Y[sup]2[/sup]

Hope that helps.
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Old 04 Mar 2010, 12:56   #3 (permalink)
Shas'O
 
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Default Re: Need maths help

Thanks, T-K, that's exactly the clarification I needed.

Back to stats.

Cheers,
Em
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Old 04 Mar 2010, 15:52   #4 (permalink)
Shas'O
 
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Default Re: Need maths help

Yeah pretty much what TK said. Although it appears to be a rather silly question because surely you would normalise all your data sets to the same units first before you started doing any statistical analysis...:P

Gen
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Old 04 Mar 2010, 18:49   #5 (permalink)
Shas'O
 
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Default Re: Need maths help

Quote:
Originally Posted by Genmotty
Yeah pretty much what TK said. Although it appears to be a rather silly question because surely you would normalise all your data sets to the same units first before you started doing any statistical analysis... :P

Gen
Yes, but this isn't real life...it's book work that is testing my ability to convert both means and standard deviations. Much of schoolwork has little to no real world application.
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Old 04 Mar 2010, 23:59   #6 (permalink)
Shas'El
 
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Default Re: Need maths help

Ah, it's just occurred to me that my original answer wasn't fully complete, Emlyn.

Let P and Q be as I defined them in my original question. Now, we established that there was a linear relationship between P and Q. I was incorrect to say that this implies that Q = aP. What I should have said was that:

Q = aP + c, for constants a and c.

Sometimes c = 0, like for example when you're converting between kilograms and pounds. There, to convert from the former to the latter you just multiply by a constant (2.2 if my memory serves me correctly.)

But to take another example, if you want to convert from degree celsius to faranheit, you have to multiply by 1.8 and then add on 32. So in this case, c = 32

So, how does this affect things:

Well, Mean(Q) = Mean(aP + c) = a*Mean(P) + c = aX + c (just as you'd expect.)

Standard deviation is slightly more interesting:

SD(Q) = SD(aP + c) = SD(aP) = a*SD(P) = aY (since adding a constant doesn't change the actual spread of the data.)

Anyway, that is the full story! I apologise for my earlier error! :P
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Old 05 Mar 2010, 00:01   #7 (permalink)
Shas'O
 
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Default Re: Need maths help

Thanks for the addendum. I was converting between centimeters and inches so no constants there.
Cheers,
Em
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