weighing avg by columns vs rows outputs different results First of all, I just know the basics of math, so please be patient. 
I have an overall score for a company with the product1 and product2. However when I do the overall for each criteria like A, B, C, D, E, the sum of these criteria is not equal to the overall score. 
Example A
Data
$\begin{array}{c|ccccc}
\;&A&B&C&D&E\\
\hline
\text{product1}&1&2&3&4&5\\
\text{product2}&2&2&3&3&3
\end{array}$
Weighing
$\begin{array}{c|ccccc}
\;&AA&BB&CC&DD&EE\\
\hline
\text{product1}&2&3&2&3&5\\
\text{product2}&2&4&3&3&4
\end{array}$
Formula for row $i$: $(A_i \times AA_i + B_i \times BB_i + \dots ) /sum(AA_i:EE_i)$

product1: $\dfrac{2+6+6+12+25}{15}=3.4$
product2: $\dfrac{4+8+9+9+12}{16}=2.625$
Total AVG: $\dfrac{3.4+2.625}{2}=3.0125$


If I try to find what is the weighing avg for each column, the total is different. Both examples should output the same weighing avg? If not, why? What is the most adequate way to represent the avg for this type of need? the first example or the second?
Example B
Formula for column $J$: $(J_1 \times JJ_1 + J_2 \times JJ_2)/sum(JJ_1:JJ_2)$
$\begin{array}{c|ccccc}
\;&A&B&C&D&E\\
\hline
\text{average}&\dfrac{2+4}{6}=1.5
&\dfrac{6+8}{7}=2
&\dfrac{6+9}{5}=3
&\dfrac{12+9}{6}=3.5
&\dfrac{25+12}{9}=4.111
\end{array}$

Total AVG: $\dfrac{1.5+2+3+3.5+4.111}{5}=2.822$


Your $2.8$ is not correct.  If you do the weighted average of $1,5\ \   2 \ \   3 \ \  3,5\ \   4$ with the weights you are using you get $3.0333333$
