Introduction to Programming $-$ Lab Manual

Statistical Analysis $($ While Loop $)$

$[$Execute this question in a new script named "Iname$\_$fname$\_$lab$4\_$stat$\_1.$m$"]$

a$)$ Problem: Implement an algorithm that reads in a set of measurements and calculates the

mean and the standard deviation of the input data set.

b$)$ Be sure your program can handle if there is $\text{'}0\text{'}$ or $\text{'}1\text{'}$ input. $($Hint: Use an if construct. If

there are less than $\text{'}2\text{'}$ inputs, display "Insufficient information" and exit. If there are

more than two inputs, go on your program.$)$

$\%$ Define variables:

$\%n--$ The number of input samples

$$dev $--$ The standard deviation of the input samples

$$ sum$\_{?}^{-}x--$ The sum of the input values

$$ sum $--$ The sum of the squares of the input values

$x-$ An input data value

$$ xbar $--$ The average of the input samples

Background

The average or arithmetic mean of a set of numbers is defined as

$\stackrel{}{x}=\frac{1}{N}{\displaystyle \underset{i=1}{\overset{N}{}}}{x}_i$

where $x_i$ is sample i out of N samples.

The standard deviation of a set of numbers is defined as

$s=\sqrt[\phantom{2}]{\frac{{\displaystyle \underset{i=1}{\overset{N}{}}}(x_i-(\stackrel{}{x}){)}^2}{N}}$

Standard deviation is a measure of the amount of scatter on the measurements; the greater

the standard deviation, the more scattered the points in the data set are.

Introduction to Programming $-$ Lab Manual

Pseudocode:

STEP $-1$: Accumulate input data

Initialize $n$ to zero, initialize array numbers$\_$x to $0$ dimension array.

Prompt user for first positive number and note that "Entering $-1$ will end the process."

Read in first $x$

while $x0$

@$,$nlarrn$+1$

@ $su{m}_x[n]=x$

sum$\_$x$[$n$]=$ x

Prompt user for next number

Read in next $x$

End

STEP $-2$: Calculate mean and Standard Deviation

$,x_{?}$bar larr sum$\_$x $/$ n

std$\_$dev larr sqrt$($ FILL IN THE BLANKS $)$

STEP $-3$: Write Out the results

Write out the mean value x$\_$bar

Write out the standard deviation std$\_$dev

Write out the number of input data points $n$

Additional Questions:

List the conditions when above program will fail.

How can you avoid these possible errors programmatically and change $"-1"$ exit flag to

any letter?