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$2=[3,2,5]$

Then weighted$\_$mean$($list$1,$ list$2)$ should return: $3(200)+2(400)+5(100)$

$3+2+5=1900$

$10=190$

$6$

Define a function named mean$()$ with two parameters named 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. The default value of w should be None. The

function should behave as follows:

$$ If w$=$None, then the function should return the standard mean $($average$)$ of the values in x$.$ You may use the

functions sum$()$ and len$()$ to calculate this.

$$ If w is a list, then the function should return the weighted mean of the values in x$,$ using the values from w as

weights.

In any case, this function should return only a single value.

The function should not print anything. It should not create any new lists, and should alter either of the lists provided

to it as arguments.

We will now test the mean$()$ function. Create a new code cell to perform the steps below.

Create the list shown below:

values $=[4,7,3,5,2,6,8,2,4,8]$

weights $=[2,1,3,1,2,3,1,4,2,1]$

Use two calls to the function mean$()$ to calculate the standard mean of values and then the weighted mean of

values, using the list weights to supply the weights. Print the results with messages as shown below.

Standard Mean: xxxx

Weighted Mean: xxxx

The call to mean$()$ that is used to calculate the standard mean is expected to involve only one argument