ESS210B
Prof. Jin-Yi Yu
Example
qWe have
four observations: [4, 1, 8, 3]
qTo
calculate the variance, we first get the mean = (4+1+8+3)/4=4
qWe then
calculate the deviations of each observations from the mean and get d = [4-4, 1-4, 8-4, 3-4] = [0, -3, 4,
-1].
qNow these
four d’s are constrained by the requirement:
d1 +
d2 + d3 + d4 =0 (a result related to the mean).
qThe
variance we get (variance = d1**2+d2**2+d3**2+d4**2) has only 3 degree of freedom ( 4 observations minus
one estimate of the parameter).