Consider the following data and corresponding weights.

Value (xi) Weight (wi)
3.2 6
2.0 3
2.5 2
5.0 8
(a) Calculate the (unweighted) mean for this variable.
(b) Now calculate the weighted mean of this variable. Notice the di erence between the
mean and the weighted mean.

a) tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

b)

And replacing we got:

Step-by-step explanation:

Part a

For this case we can calculate the the unweigthed with the following formula:

And replacing we got:

Part b

For this case the weigthed mena is given :

And replacing we got: