The formula for a 95% confidence interval is
           
(xbar-1.96*, xbar+1.96*) 

So if you add the two endpoints of a confidence interval
you will get 2xbar because the 1.96* and the
-1.96* will cancel. So you just divide the 
sum of the endpoints of the confidence interval by 2 and that 
will give you the sample mean xbar.

IOW the midpoint of the confidence interval is the sample mean,
so you just average the endpoints of the confidence interval,
and that will give the sample mean.
              
Sample mean = xbar =

Edwin