S1 question! please help! Watch

xxx-Laura-xxx
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Report Thread starter 12 years ago
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hey, i'd really appreciate you help!! i've got this question on an OCR AS level paper from November 03, Q7. I have the answers from my teacher but i don't really know how she got them!! can anyone help!?

In a science experiment, each of 12 students measured the volume of gas, xcm^3, in a particular chemical experiment. The results can be summarised:

Σ(x-50)=614 Σ(x-50)^2=32,826

i. Find the mean and standard deviation of the volumes of gas measured by the 12 students.

ans. Mean = 101 1/6
SD = 10.8

ii. Find the value of Σx^2

ans. 124226

Laura xxxx
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welwyn
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Report 12 years ago
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MEAN = (614/12) + 50 = 101.16666.. This is the real (uncoded) mean.
SD = SQRT[ (32826/12) - (614/12)^2 ] = SQRT[2735.5- 2618.027777....] = 10.838... For this sum you need to use the coded mean, ie just 614/12.

if you want to find the value of Σx^2, use the sd found before but express it in terms of the real mean. The value of the sd does not change if something is added/subtracted from the data:

sd = 10.838... = SQRT[ Σx^2/12 - 101.16666^2 ]
SO 117.472 = Σx^2/12 - 101.16666^2
SO Σx^2/12 = 10352.16666....
SO Σx^2 = 124226
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*LEGEND*
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OK so..

if you substitute (x-50) for Y, then Ey = 614 and Ey^2 = 32826
So then the mean is 614/12 = 51 and a sixth, then you add 50 (because y=x-50) to get the mean as 101 and a sixth

Then the standard deviation is 32826/12 minus 51 and a sixth^2
then square root all that lot and it should be 10.8
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xxx-Laura-xxx
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Report Thread starter 12 years ago
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aww thank uuuuuu!!!! that last question is really hard! well its gna take a while 4 me 2 learn how u do it. is it the same method for similar questions?? thanks again!!

Laura
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