So, I have multiple lists of data of different sizes. I'm calculating the average of each list. So, I have the average of each list with the total number of elements in that list.
Now I need to calculate the average of all lists. Is there a correct way to do this? I know that adding up the averages and dividing on the number of lists is correct only if all the lists are of the same size.
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1$\begingroup$ What is the average supposed to mean? 1 The average of the averages of lists 2 The average of the individual data points in the lists? $\endgroup$– Sextus EmpiricusMar 13, 2022 at 13:25
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1$\begingroup$ Example of the first case. You could be after the average of running performance of some group of people. For each person in the group you have a list of performances. Then you are not after the average of those individual performances (which is what is being computed in the answer). $\endgroup$– Sextus EmpiricusMar 13, 2022 at 13:29
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Just after I posted the question I found the Weighted Mean. I didn't know about it before.
So, I have the means of the lists, then I divide the size of each list by the sum of all sizes to get the weight for each mean.
Then I sum them all to get the weighted mean which is the correct one.
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1$\begingroup$ Follows two other references that I hope may help you to understand this problem from a bayesian point of view: Of Bayesian average and star ratings and Bayesian Average Ratings $\endgroup$– xboardSep 26, 2017 at 4:21
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1$\begingroup$ @xboard thanks for the readings. It added to my knowledge $\endgroup$– Ahmedn1Sep 27, 2017 at 14:04