mixing GROUP BY, AVG and COUNT

[Chris W]

I have a table where the date a record was added is recorded in the date 
column.  I can get count of how many records were entered on each day by 
doing this
SELECT COUNT(*)
FROM table
GROUP BY date;

I can get a total number of records by doing
SELECT COUNT(*)
FROM table
but how do I find the average count per day?  We can ignore the fact 
that it is possible that no records are added on a given day.  I almost 
for got this is on 4.0.18 so nested selects are not an option.

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Chris W
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