MySQL Average unique x for day of the week

I'm trying to get a MySQL query together to get the average amount of unique devices from a table which logs mac addresses, for each day of the week in a given month and year. So far i have this to count all devices.

SELECT DAYNAME(date_time) dow, 
DAYOFWEEK(date_time) day_num, 
COUNT( DISTINCT (mac) ) as devices
FROM detected_devices 
WHERE client_id = 11
AND venue_id = 1
AND EXTRACT( YEAR FROM date_time) = 2010
AND EXTRACT( MONTH FROM date_time) = 12
GROUP BY dow
ORDER BY day_num

Thats getting me the total number of devices but i can't seem to use the AVG function too. I've tried this line instead but get error #1111 - Invalid use of g开发者_开发问答roup function when i do.

AVG( COUNT( DISTINCT (mac) ) ) as devices

I think this is because you can't GROUP BY an alias. Try GROUP BY DAYOFWEEK(date_time) instead.