# Average deviations

1. May 25, 2005

### chynawok

Why is the average of the deviations of a set of measurement values always zero?

2. May 25, 2005

### Hurkyl

Staff Emeritus
Deviations from what?

3. May 26, 2005

### Galileo

You probably mean, why is:

$\langle X-\langle X\rangle \rangle =0$

for any distribution X. It's in the nature of the average. Use the linearity of expectations to show it.