Overall mean & standard deviation of groups of observations

Calculate the overall mean and standard deviation of groups of observations

[alln, allmean, allstd] = overallmeanstd(grpn, grpmean, grpstd)
calculates the overall number of observations (alln), the mean (allmean)
and standard deviation (allstd) of multiple groups with given number of
observations (grpn), mean values (grpmean) and standard deviations
(grpstd) for each group
this is usefull if you don't have your observations stored anymore or
you have a really high number of observations
solution comes from ...
http://www.burtonsys.com/climate/composite_standard_deviations.html

Example: copy this example (uncommented) to your command window and press enter
grp1 = [50,43,45,56]
grp2 = [65,67,50,81,83,90]
grp3 = [43,77,66,84,94,54,67]
grpn = [size(grp1,2);size(grp2,2);size(grp3,2)]
grpmean = [mean(grp1);mean(grp2);mean(grp3)]
grpstd = [std(grp1);std(grp2);std(grp3)]
grps = [grp1,grp2,grp3];
[alln, allmean, allstd] = overallmeanstd(grpn, grpmean, grpstd)
n_ = size(grps,2)
mean_ = mean(grps)
std_ = std(grps)