averageif - multiple criteria

[clock245]

This is definitely a simple question and i'm certain it's something that i'm overlooking in writing a formula, but say you have 5 values:

A1: 600
A2: 715
A3: 822
A4: 901
A5: 1001

B1: 600
B2: 950

I want to create an averageif formula. What i would like it do is to average if higher than 600, but lower than 950. So the formula i have is:
=AVERAGEIF($a$1:$a$5,"<="&B2). What am i missing for the second part -- greater than b1? For some odd reason i'm not typing the formula in correctly to get the right answer here - can anyone help

 

[tangcla]

Three sets of criteria, in total. Basically it's filtering through three columns to filter a name, a location and whether it was true, false or NA