I have several questions relate to frequency distribution that I need support. Please see my questions below and please post with examples if you can so I have more understanding.
1. Does it necessarily true that any frequency distribution contains any form of data sample? Please illustrate your answer with examples.
Skewness = E[(x-u)^3]/s^3
Here is what has been done above.
Take the definition of skewness and multiply out.
Use the fact that E(aX+bY+c) = aE(x)+bE(Y)+c (where X and Y are variables and c,a,b are constants) to simplify the expression into something we can work with.
Notation used above includes:
u = mean
s = standard deviation.
E(Y) = the expected value of Y
Note: E(X) = u in the above since u is the mean of x.
Note 2: To find E(x^n) do: E(x^n) = SUM[(midpoint of class i)*(frequency of class i)/(number of total observations)] where i ...
The solution discusses questions regarding frequency distribution and data samples.