Tutorials References Menu

Python Tutorial

Python HOME Python Intro Python Get Started Python Syntax Python Comments Python Variables Python Data Types Python Numbers Python Casting Python Strings Python Booleans Python Operators Python Lists Python Tuples Python Sets Python Dictionaries Python If...Else Python While Loops Python For Loops Python Functions Python Lambda Python Arrays Python Classes/Objects Python Inheritance Python Iterators Python Scope Python Modules Python Dates Python Math Python JSON Python RegEx Python PIP Python Try...Except Python User Input Python String Formatting

File Handling

Python File Handling Python Read Files Python Write/Create Files Python Delete Files

Python Modules

NumPy Tutorial Pandas Tutorial SciPy Tutorial

Python Matplotlib

Matplotlib Intro Matplotlib Get Started Matplotlib Pyplot Matplotlib Plotting Matplotlib Markers Matplotlib Line Matplotlib Labels Matplotlib Grid Matplotlib Subplots Matplotlib Scatter Matplotlib Bars Matplotlib Histograms Matplotlib Pie Charts

Machine Learning

Getting Started Mean Median Mode Standard Deviation Percentile Data Distribution Normal Data Distribution Scatter Plot Linear Regression Polynomial Regression Multiple Regression Scale Train/Test Decision Tree

Python MySQL

MySQL Get Started MySQL Create Database MySQL Create Table MySQL Insert MySQL Select MySQL Where MySQL Order By MySQL Delete MySQL Drop Table MySQL Update MySQL Limit MySQL Join

Python MongoDB

MongoDB Get Started MongoDB Create Database MongoDB Create Collection MongoDB Insert MongoDB Find MongoDB Query MongoDB Sort MongoDB Delete MongoDB Drop Collection MongoDB Update MongoDB Limit

Python Reference

Python Overview Python Built-in Functions Python String Methods Python List Methods Python Dictionary Methods Python Tuple Methods Python Set Methods Python File Methods Python Keywords Python Exceptions Python Glossary

Module Reference

Random Module Requests Module Statistics Module Math Module cMath Module

Python How To

Remove List Duplicates Reverse a String Add Two Numbers

Python Examples

Python Examples Python Compiler

Machine Learning - Standard Deviation


What is Standard Deviation?

Standard deviation is a number that describes how spread out the values are.

A low standard deviation means that most of the numbers are close to the mean (average) value.

A high standard deviation means that the values are spread out over a wider range.

Example: This time we have registered the speed of 7 cars:

speed = [86,87,88,86,87,85,86]

The standard deviation is:

0.9

Meaning that most of the values are within the range of 0.9 from the mean value, which is 86.4.

Let us do the same with a selection of numbers with a wider range:

speed = [32,111,138,28,59,77,97]

The standard deviation is:

37.85

Meaning that most of the values are within the range of 37.85 from the mean value, which is 77.4.

As you can see, a higher standard deviation indicates that the values are spread out over a wider range.

The NumPy module has a method to calculate the standard deviation:

Example

Use the NumPy std() method to find the standard deviation:

import numpy

speed = [86,87,88,86,87,85,86]

x = numpy.std(speed)

print(x)
Try it Yourself »

Example

import numpy

speed = [32,111,138,28,59,77,97]

x = numpy.std(speed)

print(x)
Try it Yourself »

Variance

Variance is another number that indicates how spread out the values are.

In fact, if you take the square root of the variance, you get the standard deviation!

Or the other way around, if you multiply the standard deviation by itself, you get the variance!

To calculate the variance you have to do as follows:

1. Find the mean:

(32+111+138+28+59+77+97) / 7 = 77.4

2. For each value: find the difference from the mean:

 32 - 77.4 = -45.4
111 - 77.4 =  33.6
138 - 77.4 =  60.6
 28 - 77.4 = -49.4
 59 - 77.4 = -18.4
 77 - 77.4 = - 0.4
 97 - 77.4 =  19.6

3. For each difference: find the square value:

(-45.4)2 = 2061.16
 (33.6)2 = 1128.96
 (60.6)2 = 3672.36
(-49.4)2 = 2440.36
(-18.4)2 =  338.56
(- 0.4)2 =    0.16
 (19.6)2 =  384.16

4. The variance is the average number of these squared differences:

(2061.16+1128.96+3672.36+2440.36+338.56+0.16+384.16) / 7 = 1432.2

Luckily, NumPy has a method to calculate the variance:

Example

Use the NumPy var() method to find the variance:

import numpy

speed = [32,111,138,28,59,77,97]

x = numpy.var(speed)

print(x)
Try it Yourself »

Standard Deviation

As we have learned, the formula to find the standard deviation is the square root of the variance:

1432.25 = 37.85

Or, as in the example from before, use the NumPy to calculate the standard deviation:

Example

Use the NumPy std() method to find the standard deviation:

import numpy

speed = [32,111,138,28,59,77,97]

x = numpy.std(speed)

print(x)
Try it Yourself »

Symbols

Standard Deviation is often represented by the symbol Sigma: σ

Variance is often represented by the symbol Sigma Square: σ2


Chapter Summary

The Standard Deviation and Variance are terms that are often used in Machine Learning, so it is important to understand how to get them, and the concept behind them.