MATLAB: Calculate standard deviation for different groups

Question

I want to plot a Measurement with a bar figure. Therefore I want to create different groups and calculate the standard deviation for each group. I have a vector "Measurement" which is sorted according to increasing values. I get group IDs for the Measurement values by the use of the histc function.

[~,Measure_ID]=histc(Measurement_x,0:200:max);

In the next step I try to calculate the standard deviation with the accumarray function.

group_std = accumarray(Measure_ID,Measurement_y,[],@std);

The std command uses the follow mathematical formula:

The problem is that accumarray calculates the arithmetic average for each group separately. But I want to see the standard deviation regarding to the global arithmetic average. Is there a way to solve my issue?

Version: 2012b

Answer 1

If you want to set the x_bar values of the formula to mean(Measurement_y), why not implementing this as function?

function s = specialStd(x, m)
s = sqrt(sum((x - m) .^ 2) / (length(x) - 1));
end

and call it like:

m         = mean(Measurement_x);
group_std = accumarray(Measure_ID, Measurement_y, [], @(x) specialStd(x, m));