Question

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.

Answer 1

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

And replacing we got:

`\bar X= (3.2+2.0+2.5+5.0)/(4)=3.175`

b)
`\bar X = (\sum_(i=1)^n w_i x_i)/(\sum_(i=1)^n w_i)`

And replacing we got:

`\bar X= (3.2*6+2.0*3+2.5*2+5.0*8)/(6+3+2+8)=(70.2)/(19)=3.695`

Explanation:

Part a

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

`\bar X = (\sum_(i=1)^n X_i)/(n)`

And replacing we got:

`\bar X= (3.2+2.0+2.5+5.0)/(4)=3.175`

Part b

For this case the weigthed mena is given :

`\bar X = (\sum_(i=1)^n w_i x_i)/(\sum_(i=1)^n w_i)`

And replacing we got:

`\bar X= (3.2*6+2.0*3+2.5*2+5.0*8)/(6+3+2+8)=(70.2)/(19)=3.695`