\[ X^{2}=\sum \frac{(ObservedExpected)^2}{Expected} \]



Play chess 
Not play chess 
Sum (row) 

Like science fiction 
250(90) 
200(360) 
450 

Not like science fiction 
50(210) 
1000(840) 
1050 

Sum(col.) 
300 
1200 
1500 
\[ X^{2}=\frac{(25090)^2}{90} + \frac{(50210)^2}{210} + \frac{(200360)^2}{360} + \frac{(1000840)^2} {840} = 507.93 \]
\[ a^{'}_{k} = (a_{k}mean(A))/std(A) \]
\[ b^{'}_{k} = (b_{k}mean(B))/std(B) \]
\[ correlation (A,B)=A^{'}.B^{'} \]
Correlation coefficient:
where n is the number of tuples, and are the respective mean or expected values of A and B, σA and σB are the respective standard deviation of A and B.
\[ v^{'}=\frac{vmin_{A}}{max_{A}min_{A}}(newmax_{A}  newmin_{A})+ newmin_{A} \]
\[ \frac{73,60012,000}{98,00012,000}(1.0  0)+ 0 = 0.716 \]
\[ v^{'} = \frac{v\mu_{A}}{\sigma _{A}} \]
\[ \frac{73,60054,000}{16,000} = 1.225 \]
Where j is the smallest integer such that Max(ν’) < 1