I have been working through a problem in which I am given 4 means from four different conditions, and I am also given the between, within, and total SS, df, MS and F.
I used this set of on-line directions to try to figure it out. The answer was in response to this question:
Q: The sum of 50 observations in the sample is 400. The sum of the squares is 3544. That is all I know.
How do I find variance and Standard Deviation? Do I even have enough information?
The Standard Deviation (σ) is a measure of how spread out numbers are.
σ = the square root of the Variance
so Variance (v) is the square of the standard deviation, ie: σ^2
To solve the problem, you first calculate v which will then give σ
v = The average of the squared differences from the Mean (m)
= (1/m)(sum (Xi - m)^2)
= (1/m)(sum (s)^2)
You have the number of samples (N) and their sum (T)
So you have m=(T/N) = (400/50) = 8
You have the sum of the squares(S),
S = 3544
but not the sum of the squared differences (sum (s)^2)
If you do the algebra, you can calculate σ^2 anyway by using
σ^2 = (S - (sum (s))^2/N) )/N
= ( 3544 -(160000/50) )/50
= ( 3544 - 3200 )/50 = 6.88
and the standard deviation is the square root.
Since used the average score of the four means and multiplied by the total number of subject to get an estimate of the sum of scores. I then used my sum of squares total and subtracted it from my sum of scores squared divided by my total number of subjects. After the subtraction I divided the number again by my total number of subjects and then sq rooted that number. So is this right? When I graph it, it seems as if the standard dev is way too large. Help, please.