OCR MEI Statistics 1

S_xx. Step 1
Work out the mean. X bar = Summation of x divided by n.
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Step 2
Sum of the squares (S_xx) = Summation of (x-x bar)^2 = Summation of (x^2 - n (x bar)^2)
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Mean square deviation, MSD
S_xx/n = Summation of (x^2-n(x bar)^2)/n
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What is MSD for?
It gives an average of the distance of the points away from the mean. However, the #s we get are too big because we ^2 #s to make them +ve. Hence, we use RMSD.
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What is RMSD?
It is the root mean square deviation i.e. we square root the MSD.
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What is RMSD used for?
RMSD gives us a way to look at data and compare different sets of data. We want to RMSD if we are looking at a distinct set of numbers.
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The formula of RMSD.
((Summation of x^2-n*(x-bar)^2)/n)^1/2
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MSD and RMSD is for when we are looking at a large set of data. However, what if we get a small sample of data instead?
MSD and RMSD won't work if we use a mean of the sample for a good unbiased estimator. Instead, we will use a better unbiased estimator by instead /(n-1).
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Variance and standard deviation.
Variance=(Summation of x^2-n*(x-bar)^2)/(n-1) ; Standard deviation, s=((Summation of x^2-n*(x-bar)^2)/(n-1))^1/2
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What does standard deviation tell us?
It tells us how much (on average) the data deviates from the mean (the distance from the mean to the data point).
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The larger the standard deviation is... ;The lower the standard deviation...
...the more spread out the data is. ; ...the more consistent the data is.
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Another equation to identify outliers.
(x-bar)+2*s
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Card 2

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Step 2

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Sum of the squares (S_xx) = Summation of (x-x bar)^2 = Summation of (x^2 - n (x bar)^2)

Card 3

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Mean square deviation, MSD

Back

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Card 4

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What is MSD for?

Back

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Card 5

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What is RMSD?

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