Creating an average of a list of only checked cells

Thank you up front to anyone you can help me out. I'm a numbers newbie. Basically I can't seem to figure out how to write an equation to say " give me an average of a list of numbers in column b only in there are check marks in column a next to the numbers
This is what i have but it doesn't seem to work.
=AVERAGE(IF($A$4:$A$13=TRUE,B4:B13))
I have used this equation in the past to look through a list of expenditures and total up only those rows with Gas listed
=SUM(IF($A$4:$A$13="GAS",B4:B13))
But i can't seem to get the equation to reference checkboxes
any help would be appreciated

Oops! Forgot about the average question. Let me get back...
You might be best off using the SUMIF version for TRUE cells then divide by COUNTIF(range,TRUE).
Regards,
Message was edited by: WWJD
Here's the visual:

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