# Calculation of the standard deviation of the power in dB

I wanted to find out the stability of my system so for that i calculated standard deviation of power samples data which is in dB but I am not sure whether i have used correct formula or not.

As far as I know, I can not directly take standard deviation of the dB, so i converted dB the linear using formula as follow :

After that I take a mean of this linear samples then I calculated variance after that standard deviation and finally calculated standard error and then I converted back this result into dB using following formula:

After converting back to the db the result is very strange I don't know why.

Any guidance on this matter would be highly appreciated.

• Welcome to Cross Validated! Why can’t you just take the standard deviation of the dB values?
– Dave
Jun 16 at 13:13
• Its because, If we take a standard deviation of the samples in db which which will not give you the accurate result as compare to linear that is why we should convert it first into linear.In other word, the logarithm is the most convenient way to express large numbers. The definition of logarithm can be stated as the power to which any number must be raised to obtain certain values. Jun 17 at 5:57