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SIGMA NOTATION - Need assistance

esto4273

New member
Joined
May 21, 2012
Messages
2
Below is a business metric found in a whitepaper on online communities. It aims at measuring community interaction.
My colleague and I are trying to work through the in the formula below, but we have little experience working with this level of formula.
The question we have is essentially when working through the summary notation, would you:
A) Solve for each variable, then multiply each result by the Log; finally total SIGMA
B) Total for each variable in the subquery, total then multiple the log
C) Something completely different :D

I hope you can see from the solutions we are looking at that we essentially are looking for the order which to apply the LOG and the SUM.
We would appreciate any assistance in deciphering this. Thank you.
httpwww.lithium.compdfswhitepapersLithium-Community-Health-Index_v1AY2ULb.jpg
 

srmichael

Full Member
Joined
Oct 25, 2011
Messages
848
Below is a business metric found in a whitepaper on online communities. It aims at measuring community interaction.
My colleague and I are trying to work through the in the formula below, but we have little experience working with this level of formula.
The question we have is essentially when working through the summary notation, would you:
A) Solve for each variable, then multiply each result by the Log; finally total SIGMA
B) Total for each variable in the subquery, total then multiple the log
C) Something completely different :D

I hope you can see from the solutions we are looking at that we essentially are looking for the order which to apply the LOG and the SUM.
We would appreciate any assistance in deciphering this. Thank you.
View attachment 1988
Let's say \(\displaystyle \displaystyle \Theta=3\) then, \(\displaystyle \displaystyle i=\frac{1}{3}\sum_{\theta=1}^3(u_\theta-1)log_2{m_\theta} = \frac{1}{3}[(u_1-1)log_2{m_1}+(u_2-1)log_2{m_2}+(u_3-1)log_2{m_3}]\)
 

esto4273

New member
Joined
May 21, 2012
Messages
2
Let's say \(\displaystyle \displaystyle \Theta=3\) then, \(\displaystyle \displaystyle i=\frac{1}{3}\sum_{\theta=1}^3(u_\theta-1)log_2{m_\theta} = \frac{1}{3}[(u_1-1)log_2{m_1}+(u_2-1)log_2{m_2}+(u_3-1)log_2{m_3}]\)
GREAT! So we would calculate the Log for each variable introduced. Thank you very much.
 
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