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Apologies if this is fairly straight forward. I'm looking to obtain a weighted average for categorical scores in a table based on two variables: 1) the number of users, 2) the number of transactions.

So as an example:

category score number_of_users number_of_transactions
A 4 25000 478
B 7 768 878
C 9 100 90
D 6 19000 208

If I wanted to obtain the weighted average based on number of users, it would be:

(4 x 25000) + (7 x 768) + (9 x 100) + (6 x 19000) = 220,276 / 25000 + 768 + 100 + 19000 = 44,868

220,276 / 44,868 = 4.90

However, how would I go about finding a weighted average that incorporates number of users and number of transactions? Ideally I'd like the transactions to have a greater bearing- E.G. in the table above, Category B's score would be more important than Category A's score due to the higher number of transactions.

Pheonix
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  • "Category B's score would be more important than Category A's score" : How much more important, mathematically? – user2661923 Oct 08 '21 at 12:48
  • Let's say for this case that number of users would be 0.4 and number of transactions would be 0.6 – Pheonix Oct 08 '21 at 12:51
  • Take the weighted average, based solely on the number of users. Denote this as $U$. Take the weighted average based solely on the number of transactions. Denote this as $T$. Before you can combine the two, you need a way of relating users to transactions. If you assume that $6$ users are as important as $4$ transactions, then you could simply take $(0.6)T + (0.4)U$. However, this analysis is incomplete. ...see next comment – user2661923 Oct 08 '21 at 12:56
  • Suppose that you alter the scenario, where the weighted average of transactions is still $1.5$ times as important as the weighted average of users, but that you expect each user to create $8$ transactions. Then, before you compared $U$ and $T$, you would have to normalize $T$ to $T' = \frac{T}{8}$. Not a simple issue. – user2661923 Oct 08 '21 at 12:58
  • Thanks for the information, it's given be a good basis to work from. – Pheonix Oct 08 '21 at 13:45

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