January 3

# Standard Deviation MATLAB: Everything to Know

Tandose Sambo

## Introduction to Standard Deviation Theory

The first time any science or mathematics students hear the words standard deviation, it sounds daunting. In fact, many pray that they’ll never see it again. The equation alone, for those who aren’t fans of basic calculus, is one that turns away many. For those who take the time to carefully analyze it however, the equation eventually becomes harmless. The standard deviation morphs from your worst mathematical nightmare, to becoming your statistical best friend. A key statistical term, the standard deviation is that aspect of your data collection, that allows you to identify how your data correlates to each other. Depending on what’s being done, it is helpful to identify the amount of variation in your data set. For applications that require both precision and accuracy, the standard deviation will help you in the process of your data analysis.

Represented by the equation:

Where ri is the data point, ravg the average of the data pool under analysis, and n is the number of data points in the pool. It will therefore be possible for the standard deviation to be calculated for all data sets. From the image above, analysis of a myriad of data sets has indicated that the the data will form a Gaussian distribution about a centrum or mean value. Denoted by the zero point in the data set, the rest of the data usually falls into the following categories:

1. 34.1% of the data will fall within one standard deviation from the mean (averag)
2. 13.6% of the data will fall within two standard deviations from the mean
3. 2.1% of the data will fall within two standard deviations from the mean

The aim in any statistical analysis, is to have a data set with a low standard deviation, indicating that your data is both accurate and precise, and centralized around a central point. If the data itself is spread across a wider range, then the data will have to be re-collated.

When making statistical calculations, the confidence of the analyst is often denoted by the standard deviation, as well as via additional detailed statistical tests in order to determine if the data set is statistically significant. As an initial “wet test” the data will first be tested via the standard deviation. Ideally, when data is analyzed, the analyst is anticipating a confidence interval of up to 95 percent.

The applications of this universal parameter of the standard deviation are numerous. Every field that falls into the category of mathematics, science and engineering utilizes this data. Insurance premium calculations, investment strategies, engineering control averages, and a myriad of other functions will utilize the standard deviation. Knowing that the parameter is critical to know, in this lesson you will learn:

1. What is Standard Deviation MATLAB – the syntax used by MATLAB in order to calculate the relevant data variance details
2. How to calculate the Standard Deviation using MATLAB Without any further ado, let us jump into the tutorial.

## Introduction to Standard Deviation MATLAB

The standard deviation MATLAB function is that aspect of the MATLAB syntax toolbox, that enables the user to calculate the standard deviation or the variance of a data pool. The MATLAB system is a powerful tool and provides more than one means via which the parameter can be carried out. The following are the options that are available for the user:

S = std(A)

S = std(A,w)

S = std(A,w,’all’)

S = std(A,w,dim)

S = std(A,w,vecdim)

S = std(___,nanflag)

Let us define each of the parameters so that as a user, you can determine the option that will work best for you.

S = std(A) is the option that will generate the standard deviation of the elements of A. The focus is on the first array dimension, for parameter not equal to 1. The MATLAB system will focus on calculating the standard deviation of vectors, matrices, and also multi-dimensional arrays.

S = std(A,w) is the MATLAB option that provides a weighting of the various syntaxes available in the system. The user will define what weight the critical parameters will be. The function of the weightings will be in the normalizing of the final Gaussian distribution generated by the system. Since filters can be generated by the system, this is one means via which the user can find the relevant control to facilitate the desired output.

S = std(A,w,’all’) is an option that utilizes a w of either 0 or 1 in order to determine its final value.

S = std(A,w,dim) is another weighted calculation that returns the standard deviation with a focus on the dimension, dim. It is a normalizing function, that operates best when w=0.

S = std(A,w,vecdim)is the standard deviation function normalized over the dimension of the vector, vecdim. The weighting for w is either 0 or 1.

S = std(___,nanflag) is the sixth option, which focuses on options that are not numbers. This occurs when a data set may contain a mix of alpha numeric data, and the analyst would like the option to filter through the data, and find the standard deviation of the numbers.

With all this knowledge under our belts, let us jump into the practical portion of the exercise. As usual, now’s the time to turn on your system, and see how best you can apply this good knowledge! Knowledge is power!!!

## Brief Tutorial: Standard Deviation MATLAB

The first step of the exercise is to log into the MATLAB system. For the purposes of this tutorial, the R2019a version of MATLAB will be utilized. Opening a fresh command window, the following is your welcome screen:

With the system up and running, we can now dive into the calculation pool. Only the real statisticians crave the thrill that comes from having accurate and precise data…so let’s be that. As of now…you’ll transform in that motivated version of yourself…that loves statistics. Let’s do this! From the MATLAB workbook, we will start our first objective.

As a matrix-based system, let us work with the first objective involving finding the standard deviation of matrix columns. Your task will be to:

Create a matrix and compute the standard deviation of each column.

A = [4 -5 1; 2 3 5; -9 1 7];

S = std(A)

The first line of code contains the data for the matrix function A. From our syntax pool outlined above, we will begin with the first equation. Enter the code into the MATLAB Command Window, and then press enter. When Matlab works its magic, the following is the data that is generated:

Congratulations, you have calculated your first standard deviation in MATLAB. Based on the fact that three values are generated, is indicative of the fact that the matrix has three columns. The system will automatically silo the columns, and find the standard deviation of each one. With the advanced adjusters identified in the syntax, the user can determine if the entire pools standard deviation should be calculated.

With your confidence boosted, let us calculate the next data set, with the appropriate weightings in the data set.

Objective: Create a matrix and compute the standard deviation of each column according to a weight vector w.

A = [1 5; 3 7; -9 2];…(1)

w = [1 1 0.5];…(2)

S = std(A,w)…(3)

Let us dissect this code line by line. The first line of code is our data set.This is an array with three columns, and two rows. The weightings, are given for the three columns. It can be seen that the first two columns have equal weightings, while the final column has half the weightings of the column.

The system will calculate the relevant data, and then produce the final image above, with the critical answer. Since three weightings were given, and only two data values are generated, the system is indicating that the third column is insignificant.

## CONCLUSIONS

As you work your way through the system, you’ll be able to identify the syntax that will be relevant to your statistical needs. For your various science and engineering needs, the statistical tool of a standard deviation will be critical to your data integrity. Since science requires validation as proof of the integrity of the data, knowing that your data is accurate to up to 95% of the time, will ensure that as an analyst, you are confident in your presentation. With the power of MATLAB, there is so much that you can do in the quest for number crunching, and converting that data into useful information. With your adroit mathematical skills, you just might be the one to discover a process that is life-changing.

#### Reference Articles:

1. Wikipedia: https://en.wikipedia.org/wiki/Standard_deviation
2. Standard Deviation MATLAB: https://www.mathworks.com/help/matlab/ref/std.html

Tandose Sambo is a Chemical Process Engineer, with a focus on improving process efficiency via operational improvements. Six-Sigma certified, and with a Design-focus and Data Analytics interest, she is a driven growing entrepreneur, with the intention to optimize industrial and business process operations. Her interests include sharing time with family and travelling.

Tandose Sambo