Create a markdown cell with a level $1$ header that reads: "DSCI $303-$ Homework $05".$ Add your name below that as a level $3$

header

Import the following packages: numpy, math, and matplotlib.pyplot. No other packages should be used in this project.

Problem $1$: Sample Mean and Variance

In this problem, you will be asked to use NumPy to calculate sample mean and variance of a data set in two ways:

$1.$ First using numpy to perform the calculations indicated by the formulas for these values, and

$2.$ Then using built$-$in NumPy functions for the mean and variance.

We start with a discussion of the necessary formulas. Given a collection of $$ numerical observations $1,2,...,,$ the

sample mean $$ and sample variance $2$ of the observations are given by the following formulas:

$$ Sample mean: $=1$

$$

$$

$=1=1$

$(1+2++)$

$$ Sample variance: $2=1$

$1()2$

$=1=1$

$1[(1)2+(2)2++()2]$

Create a code cell to perform the following steps:

$1.$ Create an array x containing the following integers: $10,16,26,12,17,22,14,12,21,16$

$2.$ Store the length of this array in a variable n$.$

$3.$ Calculate the sample mean, storing the result in mean. You may use np$.$sum$()$ in your calculation.

$4.$ Calculate an array named diff that stores the differences between each value in x and the mean. That is to

that that diff should contain values $()$ for each$=1,...,.$

$5.$ Use diff, n$,$ and np$.$sum$()$ to find the sample variance. Store the result in a variable named var.

$6.$ Print your results in the format shown below. Make sure that the numerical outputs are aligned with each other

on the left.

Sample Mean: xxxxx

Sample Variance: xxxxx

Your code in Problem $1$ should not include any loops.