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Variance

Explanations > Social Research > Statistical principles > Variance

Description | Example | Discussion | See also

Description

Variance is a measure of the spread in a list of numbers. It is commonly represented as s² or s² (sigma-squared).

It is calculated as follows for a sample:

VAR(X) = SS/(N-1)

= (SUM(X_i - AVERAGE(X))) / (N-1)

where N is the number of items in the list.

If the list represents a complete population, then the division is by N (not N-1).

VAR(X) = SS/N

= (SUM(X_i - AVERAGE(X))) / N

Example

A set of measures, as in Column A below, can easily have its variance calculated.

	Column A	Column B	Column C

	x	x - x-bar	(x - x-bar)^2
	5	0.25	0.0625
	6	1.25	1.5625
	2	-2.75	7.5625
	8	3.25	10.5625
	3	-1.75	3.0625
	5	0.25	0.0625
	2	-2.75	7.5625
	7	2.25	5.0625

number of measures, n:	8
sum of measures:	38
average, x-bar:	4.75

Sum of squares, SS:			35.5
Variance, s^2 = SS/(N-1):			5.071429

Discussion

Variance is an improvement on Sum of the Squares, SS, as a measure of spread, as it makes the measure independent of the length of the list of numbers.

Dividing SS by (N-1) is due to the 'degrees of freedom' issue.

Variance is a part of many other calculations, from standard deviation to ANOVA.

Variance has the disadvantage that it is measured in squared units as compared with the number in the original list. This is why it is represented as s^2, as sigma represents the standard deviation.

In Microsoft Excel, the formula VAR() may be used to automatically calculate the variance of a range of measures.

See also

Variation, Sum of the Squares, SS, The Test Statistic

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Site Menu

| Home | Top | Quick Links | Settings |

Main sections: | Disciplines | Techniques | Principles | Explanations | Theories |

Other sections: | Blog! | Quotes | Guest articles | Analysis | Books | Help |

More pages: | Contact | Caveat | About | Students | Webmasters | Awards | Guestbook | Feedback | Sitemap | Changes |

Settings: | Computer layout | Mobile layout | Small font | Medium font | Large font | Translate |

Please help and share:

Quick links

Disciplines

* Argument
* Brand management
* Change Management
* Coaching
* Communication
* Counseling
* Game Design
* Human Resources
* Job-finding
* Leadership
* Marketing
* Politics
* Propaganda
* Rhetoric
* Negotiation
* Psychoanalysis
* Sales
* Sociology
* Storytelling
* Teaching
* Warfare
* Workplace design

Techniques

* Assertiveness
* Body language
* Change techniques
* Closing techniques
* Conversation
* Confidence tricks
* Conversion
* Creative techniques
* General techniques
* Happiness
* Hypnotism
* Interrogation
* Language
* Listening
* Negotiation tactics
* Objection handling
* Propaganda
* Problem-solving
* Public speaking
* Questioning
* Using repetition
* Resisting persuasion
* Self-development
* Sequential requests
* Storytelling
* Stress Management
* Tipping
* Using humor
* Willpower

Principles

Explanations

* Behaviors
* Beliefs
* Brain stuff
* Conditioning
* Coping Mechanisms
* Critical Theory
* Culture
* Decisions
* Emotions
* Evolution
* Gender
* Games
* Groups
* Habit
* Identity
* Learning
* Meaning
* Memory
* Motivation
* Models
* Needs
* Personality
* Power
* Preferences
* Research
* Relationships
* SIFT Model
* Social Research
* Stress
* Trust
* Values

Theories

* Alphabetic list
* Theory types

And

– About
– Guest Articles
– Blog!
– Books
– Changes
– Contact
– Guestbook
– Quotes
– Students
– Webmasters

| Home | Top | Menu | Quick Links |

© Changing Works 2002-
Massive Content — Maximum Speed