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I've been for a while in the Mathematics site, and I'm curious about the high reputation some people have. I like the feeling of being proud about a number representing how much you've contributed to people on the site.

My questions is, is there any page with information about the "average reputation" of the people active in the forum? I don't know if it's one of the moderator tools, or if it doesn't even exist, but I'm just curious about it. Is there any data out there about that? Thanks.

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    $\begingroup$ This rather depends on what you mean by people active in forum. (Probably site would be a better terminology than forum.) I will still mention that some distribution of users by the reputation can be seen in the reputation league: stackexchange.com/leagues/69/alltime/math $\endgroup$ – Martin Sleziak Jul 6 at 10:10
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As I mentioned in a comment, you can see some kind of distribution of users by reputation in the reputation league. (Notice the table on the right. Reputation leagues is also linked from the thingy in your profile which says "top x% this week/month...")

If you want to calculate average reputation, you can use SEDE. This is a useful tool which can be used to get various data about Stack Exchange using SQL.

For example, here is a query calculating average reputation. However, I would imagine that you might prefer to eliminate users who never posted anything on the site. So maybe it would be reasonable to add some restrictions. You may notice that the query has a parameter min, by changing this parameter you will be looking at users above some threshold. For example, the same query for users having at least 101 reputation points.

And if you increase it a bit more, the average increases quite rapidly - here is the result for 102 and for 125. The reason for the big jump between 101 and 102 is that there are many users who never posted anything and all their reputation comes from the association bonus. (Which leaves them at exactly 101 reputation points.)

Similarly, we see - as expected - rather big jump between looking at average of all users and users with reputation at least 2 - since the latter includes the users who did at least some reputation-related action on the site or have the association bonus.

We should also keep in mind that users who are currently suspended have reputation 1. There are some users with many posts which are suspended at the moment - this also influences the average. Without the suspension, those users would contribute with reputation much higher than 1.

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    $\begingroup$ It's interesting that once you reach a 1000 points, the average is 6000+, but over 10k we only reach 38k or so on average. I wish we could break this down by length of time since registration, number of questions, answers, bounties, etc. $\endgroup$ – Asaf Karagila Jul 6 at 13:40
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    $\begingroup$ @AsafKaragila As it happens, some time ago I created a query showing average reputation depending on the age of the account in months: data.stackexchange.com/math/query/1241593/… (I hope I did not make some mistake there.) If there are some other queries which can be clearly specified and which are not beyond my abilities, I might try - but I cannot promise anything for sure. (Perhaps it might be better to discuss them in chat - as not to leave too many comments here.) $\endgroup$ – Martin Sleziak Jul 6 at 13:47
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    $\begingroup$ For anyone who doesn't feel like running the mentioned SEDE queries to get current data: as of when I posted this comment (July 6th, 2020), the average reputation was 123.5, the average of those with reputation >=2 was 269.7, reputations >=101 average 543.5, and reputation >=102 average 889.7. $\endgroup$ – Milo Brandt Jul 6 at 22:47
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    $\begingroup$ I take it all these "averages" are arithmetic means. Anyone keen to calculate the mode? median? geometric mean? harmonic mean? $\ell^2$-norm? standard deviation? $\endgroup$ – Gerry Myerson Jul 7 at 3:29
  • $\begingroup$ @GerryMyerson I think that to do such computations it might be better not to do them directly in SQL, but to download the data and do them in some other software. I think this might be difficult to do in SQL - at least I can say for sure that it is beyond my knowledge of SQL. $\endgroup$ – Martin Sleziak Jul 7 at 3:48
  • $\begingroup$ I have at least tried to find median, using the method suggested in Jeff Attwood's answer: Function to Calculate Median in SQL Server. Assuming that I did not make some mistake, median is equal to 1. I guess this was expected. Again, we can restrict this to users above some threshold, for example at least 102 reputation (removing all users who only have repuataion from the association bonus.) $\endgroup$ – Martin Sleziak Jul 7 at 3:48
  • $\begingroup$ I have added some other SEDE queries in chat: chat.stackexchange.com/rooms/19138/conversation/… Only a few, since I do not have much time to spend with this right now. This was partly in the response to @AsafKaragila's suggestion to get some breakdown based on number of posts. $\endgroup$ – Martin Sleziak Jul 7 at 3:59

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