Problem $8$: Weighted Means

In this problem, we will create a function named mean$()$ that can be used to calculate either standard means or weighted

means. The function will have two parameters, x and w$.$ The parameter x is expected to be a numerical list, and w is

expected to be either a numerical list or to have the value None. If w$=$None, then the function should simply return the

mean $($or average$)$ of the elements in x$.$ If w is a list, then the function should return the weighted mean of the elements in

x$,$ using the elements of w as weights.

If the elements of x are denoted by $0,1,...,$ and the elements of w are denoted by $0,1,...,,$ then the weighted

mean is calculated as follows:

$$

$00+11++$

$$

$0+1++$

As an example $($that you are not being asked to include in your notebook$),$ if:

list$1=[200,400,100]$

list$2=[3,2,5]$

$3(200)+2(400)+5(100)1900$

Then weighted$\_$mean$($list$1,$ list$2)$ should return: $==190$

$3+2+5$

$10$

$5$

$\backslash$