There are a variety of ways to do this, all more or less involving creating a grouping variable that says what minute each row of your data are from. From there, you can use things like varfun (on a table), splitapply, or accumarray to compute the means in each group.
Since R2014b, you could use durations to represent the elapsed time.
In the recently-released R2016b, you can use timetables to do this in one line of code:
% given t and x as the two columns of data, make a timetable
>> tt = timetable(x,'RowTimes',t)
tt =
Time x
_________ ____
12.354 hr 23.1
12.356 hr 24.5
12.357 hr 22.9
12.359 hr 23.8
12.361 hr 25.2
[snip, 110 more rows]
>> tt.Time.Format = 'm'
tt =
Time x
__________ ____
741.23 min 23.1
741.34 min 24.5
741.44 min 22.9
741.54 min 23.8
741.64 min 25.2
[snip, 110 more rows]
>> ttm = retime(tt,'minutely','mean')
ttm =
Time x
_______ ______
741 min 23.75
742 min 24.55
743 min 26.433
744 min 26.75
745 min 26.067
746 min NaN
747 min NaN
[snip, 19 more rows]
