Test 3 - Q1-G - Applied Statistics Forum

Test 3 - Q1-G

Student

Hello, when i try to calculate S², i go from the definition to (1/n-1) *( Sum(i=1, n, X²_i) + 2*X_barre*Sum(i=1, n, X_i) + Sum(i=1, n, X²_barre)). Then by using the fact that 1/n*Sum(i=1, n, X_i) = X_barre, i can say that Sum(i=1, n, X_i) = n*X_barre.
So i get (1/n-1) * (9.7 - 2*2.5*16*2.5 + 16 * 2.5) but it is negative thus i must have a mistake but i don't know where.

Thanks for your help.

Teacher

Use the decomposition
\sum_i(X_i-\overline{X})^2=\sum_i X_i^2-n\overline{X}^2
A square is missing in your third term.

Student

I don't understand how we get this decomposition. Because for me, we have to use the identity.

Teacher

\sum_i(X_i-\overline{X})^2=\sum_i(X_i^2-2X_i\overline{X}+\overline{X}^2)=\sum_iX_i^2-2\overline{X}\sum_iX_i+\sum_i\overline{X}^2=\sum_iX_i^2-2n\overline{X}^2+n\overline{X}^2
hence the decomposition.

Student

Thanks got the decomposition but I still find a negative result for S, is it normal ?

A free forum powered by FreeFlarum.com (remove this footer)
Terms & Conditions | Report This Forum | Privacy Policy