I'm looking at some Facebook advertising data. It has a row for each ad and the upper and lower bounds of the impressions for that ad (i.e. number of times it was displayed). For example:

 ad_id     impressions_lower      impressions_upper
 1         0                      999
 2         1000000                NaN # No upper bound stated 
 3         2000                   2999
 4         35000                  35999
 5         0                      999
 6         1000                   1999
 7         0                      999
 8         0                      999
 9         0                      999

I want to estimate roughly how many times each ad was viewed, as a single number, to give a rough idea of the distribution of impressions and the total number of impressions.

I could take the simple midpoint of the impressions and use that.

But the overall distribution of the data is not normal: there are many more ads with a small number of impressions than with a large number of impressions. I guess it's a Poisson distribution?

So perhaps I should pick, say, 20% of the way along the range; or 30% along; or 40%. I'm not a statistician, but I feel that there must be a way to choose what's a reasonable number.

Of course, I will report the upper and lower error bars too: but it would be very useful to have a reasonable, rule-of-thumb single estimate for number of impressions for each ad.


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