Determining std dev with errors in measurements

[karna87]

I have the following sample of measurements "V" and each has error "E" incorporated in the measurement. If I want to take mean of the sample how should I proceed. I figure that I can compute "sigma" by taking square root of the (sum of square of deviations from the mean divided by the number of sample-1). but that sigma will not incorporate the "E" errors inherent in the "V"

V E

6 1
5 0.2
4 3
6 2

I can compute mean and stddev suing Matlab, but how do I incorporate "E" in the computation.

thanks,

 

[Bill Simpson]

Hint:
Assuming your error is uniformly distributed, if not adjust accordingly.
Suppose you have a horizontal bar one unit high and
centered at 6 and 1 unit wide
centered at 5 and 0.2 unit wide
centered at 4 and 3 unit wide
centered at 6 and 2 unit wide.
Does that correctly represent your data? Or do they need to be other than one unit high?
Can you perhaps think "center of gravity" to then calculate your mean?
Can you perhaps think of another calculation to then calculate your standard deviation?

 

[karna87]

thanks for your help !