# How to find the standard deviation of an instrument when ameasurement cannot be repeated

Discussion in 'Probability' started by Misterbeets, Dec 9, 2011.

1. ### MisterbeetsGuest

I have a problem that I'm hoping someone can help with. Suppose I measure the velocity of many fastballs with two nominally identical radar guns. For each pair of measurements I calculate a standard deviation, and from these an overall average SD. Assuming there is no systematic error, and the SD isthe same for each gun, have I found the SD for either one?

Misterbeets, Dec 9, 2011

2. ### Ray KoopmanGuest

The average of the SDs of the pairs of measurements will usually
be a severe underestimate of the true SD, and taking lots of pairs
won't cure the problem.

The square root of the average variance will usually be closer
to the true SD, and it will get more accurate as you increase
the number of pairs.

Ray Koopman, Dec 10, 2011