Statistics

Standard Deviation to Variance

Published by
Mike Woodhill PhD




Standard Deviation to Variance Calculator


Solution:

Enter the Standard Deviation in the above Box.
Next, press Solve to find the Variance.


What is the difference between Variance and Standard Deviation?

Both Variance and Standard Deviation are Measures of Spread in Statistics.
The Variance is the Sum of the Squared Differences between the given Data and their Mean.
Taking the Square-Root of the Variance then gives the Standard Deviation. The Standard Deviation tells us by how much the data differ from the mean, the average distance from the mean. As formulas:


Example for computing both Variance and Standard Deviation?

Say we are given 2,3,4. Their mean is 3 since (2+3+4)/3 = 3 .
The Squared Differences between the data and mean are
(2-3)² + (3-3)² + (4-3)² = 1+0+1=2 .
Dividing that by the number of data points, here 3, yields s²=2/3=0.666 as the variance.
Finally, take the Square Root of the Variance to find the Standard Deviation
s= √(s²)=(0.666)=0.81649658092 .

How do you find Variance from Standard Deviation?

To find Variance we have to Square the Standard Deviation.
Reason: Standard Deviation is s , the Variance is .

How do you find Standard Deviation from Variance?

To find Standard Deviation we have to take the Square Root of the Variance.
Reason: The Variance is , the Square of the Standard Deviation is s .

What is the Difference between Population Variance and Sample Variance?

When computing Population Variance we divide by the Population Size N (as shown in the image above).
When computing Sample Variance we divide by the Sample Size N-1 instead (for technical reasons) .

Mike Woodhill PhD

As a long time instructor I would like you to benefit from my Step by Step Calculators. You may also schedule a live tutoring session to succeed in your class. 😉

Published by
Mike Woodhill PhD

Recent Posts

  • uncategorized

LaPlace Transform Calculator

Laplace Transform Calculator Enter your Function in terms t to find any Laplace Transform. How…

9 months ago
  • Parabola

Parabola Graphing Calculator

What is the purpose of the Parabola Graphing Calculator? It allows you to graph Parabolas.…

9 months ago
  • Mike

Contact Mike

For Questions, Bookings, etc : Chat with us. Email us : support@mikescalculator.com Or call us…

9 months ago
  • Tutoring

Schedule a Tutoring Session

For Questions, Bookings, etc : Chat with us. Email us : support@mikescalculator.com Or call us…

9 months ago
  • Quadratic Equations

Domain and Range of a Parabola

Table of Content (8 min. reading time) 1 - Step by Step Solver: Find the…

9 months ago
  • Algebra

Domain and Range Calculator

What is the Domain and Range? 1) The Domain is defined as the set of…

9 months ago
  • Statistics

What is the Mean in Math?

What does the Mean mean in Math? The Mean in Mathematics is just another word…

9 months ago
  • Statistics

Sample Standard Deviation

What is the Formula for Sample Standard Deviation ? The Formula for the Standard Deviation…

9 months ago
  • Statistics

Mean Median Mode Range Calculator

How do you find Mean, Median, Mode, Range, Standard Deviation and Variance? Mean = Average…

9 months ago
  • Algebra

Compute Discriminant – to discriminate between Real and Complex Solutions of a Quadratic Equation.

What you will learn in this mini lesson You will learn how to find the…

9 months ago
  • Algebra

How to Factor a Quadratic Equation and Solve It.

What you will learn in this mini lesson You will learn how to factor and…

9 months ago
  • Algebra

Standard Form of a Quadratic Function

What you need to know about Standard Form of a Quadratic Function The Quadratic Equation…

9 months ago
  • Vertex

Vertex Form in 5 Minutes (Formulas, Solvers, Examples)

What is Vertex Form of a Quadratic Equation? The Vertex Form is f(x) = a(x-h)²+k…

9 months ago
  • Algebra

Solve A Quadratic Equation by Completing the Square

What you will learn in this mini lesson You will learn how to solve Quadratic…

9 months ago
  • Algebra

STANDARD TO VERTEX FORM CALCULATOR

Table of Content (8 min. reading time) 1 - Step by Step Solver: Find the…

9 months ago
  • Vertex Form of a Parabola

VERTEX TO STANDARD FORM CALCULATOR

How to convert from Vertex to Standard Form? The Vertex Form of a Parabola is…

9 months ago
  • Quadratic Equations

The 3 Parabola Forms: Standard Form, Vertex Form and Factored Form.

What you will learn in this mini lesson You will learn how the 3 different…

1 year ago
  • Algebra

Quadratic Form Calculator

What you will learn in this mini lesson You will learn how to solve Quadratic…

2 years ago
  • Python

Python Random Number Generator

How to generate Random Numbers using Python's Random Number Generator. 1) Let's start with an…

2 years ago