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Graduation - Individual Standardised Deviations Test

C

CorkActuary

Member
You know where you are comparing the Expected with the observed interval readings to see whether or not there is a skewness in standard deviations.. Where are the expected values derived from? Are there something to do with distribution of standard curve?

E.g.
Interval: (-3,-2) (-2,-1) (0,-1) (0,1) (1,2) (2,3)
Expected: 0.2 1.4 3.4 3.4 1.4 0.2
Observed: 0 0 6 2 2 0

There is an obvious symmetry to the expected values but from where are they derived?
 
In a normal distribution, you expect roughly 68% values to lie between (mu - sigma) and (mu +sigma).
In the standard normal case, mu =0, sigma =1.
Therefore you should have 68% values in (-1,1).
Due to symmetry, 34% should lie within (-1,0) and another 34% in (0,1).

In your case you would have in all 10 values. So 3.4 each in (-1,0) and (0,1).
Then look at (mu-2 sigma) to (mu +2 sigma).
Here you should have 96% of all the values.
Hence the next 14% from (-2,-1) and (1,2)
and so on...
 
Thanks... Hopefully, different parameter values for mu and sigma won't be asked... :(
 
Cheer up!! they wont!! You are expected to compare the values with a standard normal curve!! :)
 
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