Any formula or script to combine standard deviation of different group into one standard deviation

[#1]

Hi all,

Currently, I was stuck to combining standard deviation from different group into one standard deviation.
For example
A) sample = 50, mean = 5, standard deviation = 3

B) sample = 40, mean = 6, standard deviation =2

C) sample = 20, mean = 7, standard deviation =4

How I can combine standard deviation from 3 groups into one. Is there any function available in JMP to support this?
Thank a lot 

[#2]

Variances add, standard deviations do not.  Square the standard deviations, add them, take the average.  Then take the root.