How do I generate a series of hourly averages in MySQL?

There is also another possibility considering the fact that dates have a string representation in the database:

You can use SUBSTRING(thetime, 1, [len]), extracting the common part of your group. For the example with hourly averages you have the SQL query

SELECT SUBSTRING(thetime, 1, 13) AS hours, AVG(value) FROM hourly_averages GROUP BY hours

By the len parameter you can specify the aggregated time interval considering the MySQL date format yyyy-MM-dd HH:mm:ss[.SS...]:

• len = 4: group by years
• len = 7: group by months
• len = 10: group by days
• len = 13: group by hours
• len = 16: group by minutes
• len = 19: group by seconds

We encountered a better performance of this method over using date and time function, especially when used in JOINs in MySQL 5.7. However in MySQL 8 at least for grouping both ways seem to take approximately the same time.

This should work:

SELECT AVG( value ) , thetime
FROM hourly_averages
GROUP BY HOUR( thetime )

Here's the result

AVG(value)          thetime
5.4166666865349     2009-01-26 00:00:00
8.8666666348775     2009-01-26 01:00:00
3.5                 2009-01-26 02:00:00

It's unclear whether you want the average to be aggregated over days or not.

If you want a different average for midnight on the 26th vs midnight on the 27th, then modify Mabwi's query thus:

SELECT AVG( value ) , thetime
FROM hourly_averages
GROUP BY DATE( thetime ), HOUR( thetime )

Note the additional DATE() in the GROUP BY clause. Without this, the query would average together all of the data from 00:00 to 00:59 without regard to the date on which it happened.