# Connexions

You are here: Home » Content » Elementary Statistics » Summary of Formulas

• Student Welcome Letter

• 13. Tables

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Endorsed by (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
• College Open Textbooks

This module is included inLens: Community College Open Textbook Collaborative
By: CC Open Textbook CollaborativeAs a part of collection: "Collaborative Statistics"

"Reviewer's Comments: 'I recommend this book. Overall, the chapters are very readable and the material presented is consistent and appropriate for the course. A wide range of exercises introduces […]"

Click the "College Open Textbooks" link to see all content they endorse.

Click the tag icon to display tags associated with this content.

• JVLA Endorsed

This module is included inLens: Jesuit Virtual Learning Academy Endorsed Material
By: Jesuit Virtual Learning AcademyAs a part of collection: "Collaborative Statistics"

"This is a robust collection (textbook) approved by the College Board as a resource for the teaching of AP Statistics. "

Click the "JVLA Endorsed" link to see all content they endorse.

• WebAssign

This module is included inLens: WebAssign The Independent Online Homework and Assessment Solution
By: WebAssignAs a part of collection: "Collaborative Statistics"

"Online homework and assessment available from WebAssign."

Click the "WebAssign" link to see all content they endorse.

Click the tag icon to display tags associated with this content.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• OrangeGrove

This module is included inLens: Florida Orange Grove Textbooks
By: Florida Orange GroveAs a part of collection: "Collaborative Statistics"

Click the "OrangeGrove" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

• Bookshare

This module is included inLens: Bookshare's Lens
By: Bookshare - A Benetech InitiativeAs a part of collection: "Collaborative Statistics"

"DAISY and BRF versions of this collection are available."

Click the "Bookshare" link to see all content affiliated with them.

• Featured Content

This module is included inLens: Connexions Featured Content
By: ConnexionsAs a part of collection: "Collaborative Statistics"

"Collaborative Statistics was written by two faculty members at De Anza College in Cupertino, California. This book is intended for introductory statistics courses being taken by students at two- […]"

Click the "Featured Content" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

#### Also in these lenses

• statistics

This module is included inLens: Statistics
By: Brylie OxleyAs a part of collection: "Collaborative Statistics"

Click the "statistics" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Lucy Van Pelt

This module is included inLens: Lucy's Lens
By: Tahiya MaromeAs a part of collection: "Collaborative Statistics"

"Part of the Books featured on Community College Open Textbook Project"

Click the "Lucy Van Pelt" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Educational Technology Lens

This module is included inLens: Educational Technology
By: Steve WilhiteAs a part of collection: "Collaborative Statistics"

Click the "Educational Technology Lens" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Statistics

This module is included inLens: Mathieu Plourde's Lens
By: Mathieu PlourdeAs a part of collection: "Collaborative Statistics"

Click the "Statistics" link to see all content selected in this lens.

• statf12

This module is included inLens: Statistics Fall 2012
By: Alex KolesnikAs a part of collection: "Collaborative Statistics"

Click the "statf12" link to see all content selected in this lens.

• UTEP

This module is included inLens: Amy Wagler's Lens
By: Amy WaglerAs a part of collection: "Collaborative Statistics"

Click the "UTEP" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Make Textbooks Affordable

This module is included inLens: Make Textbooks Affordable
By: Nicole AllenAs a part of collection: "Collaborative Statistics"

Click the "Make Textbooks Affordable" link to see all content selected in this lens.

• BUS204 Homework

This module is included inLens: Saylor BUS 204 Homework
By: David BourgeoisAs a part of collection: "Collaborative Statistics"

"Homework for Discrete Variables/Probability. "

Click the "BUS204 Homework" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• crowe

This module is included in aLens by: Chris RoweAs a part of collection: "Collaborative Statistics"

Click the "crowe" link to see all content selected in this lens.

• Bio 502 at CSUDH

This module is included inLens: Bio 502
By: Terrence McGlynnAs a part of collection: "Collaborative Statistics"

"This is the course textbook for Biology 502 at CSU Dominguez Hills"

Click the "Bio 502 at CSUDH" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection (Textbook):

Textbook by: Kathy Chu, Ph.D.. E-mail the author

# Summary of Formulas

Summary: A summary of useful formulas used in examining descriptive statistics

## Commonly Used Symbols

• The symbol ΣΣ means to add or to find the sum.
• nn = the number of data values in a sample
• NN = the number of people, things, etc. in the population
• x¯x¯ size 12{ {overline {x}} } {} = the sample mean
• ss = the sample standard deviation
• μμ = the population mean
• σσ = the population standard deviation
• ff = frequency
• xx = numerical value

## Commonly Used Expressions

• x*fx*f = A value multiplied by its respective frequency
• xx size 12{ Sum {x} } {} = The sum of the values
• x*fx*f size 12{ Sum {x} times f} {} = The sum of values multiplied by their respective frequencies
• ( x x ¯ ) (x x ¯ ) or ( x μ ) (xμ) = Deviations from the mean (how far a value is from the mean)
• ( x x ¯ ) 2 ( x x ¯ ) 2 or ( x μ ) 2 ( x μ ) 2 = Deviations squared
• f ( x x ¯ ) 2 f ( x x ¯ ) 2 or f ( x μ ) 2 f ( x μ ) 2 = The deviations squared and multiplied by their frequencies

Mean Formulas:

• x¯=x¯= size 12{ {overline {x}} ={}} {}xnxn size 12{ { { Sum {x} } over {n} } } {} or x¯=x¯= size 12{ {overline {x}} ={}} {}f· xnf· xn size 12{ { { Sum {f times x} } over {n} } } {}
• μ=μ= size 12{μ={}} {}xNxN size 12{ { { Sum {x} } over {N} } } {} or μμ size 12{μ} {}= f·xNf·xN size 12{ { { Sum {f times x} } over {N} } } {}

Standard Deviation Formulas:

• s=s= size 12{s={}} {} Σ ( x x ¯ ) 2 n 1 Σ ( x x ¯ ) 2 n 1 or s=s= size 12{s={}} {} Σ f · ( x x ¯ ) 2 n 1 Σ f · ( x x ¯ ) 2 n 1
• σ=σ= size 12{σ={}} {} Σ ( x μ ¯ ) 2 N Σ ( x μ ¯ ) 2 N or σ=σ= size 12{σ={}} {} Σ f · ( x μ ¯ ) 2 N Σ f · ( x μ ¯ ) 2 N

Formulas Relating a Value, the Mean, and the Standard Deviation:

• value = mean + (#ofSTDEVs)(standard deviation), where #ofSTDEVs = the number of standard deviations
• xx size 12{x} {} = x¯ x + (#ofSTDEVs)(ss)
• xx size 12{x} {} = μμ size 12{μ} {} + (#ofSTDEVs)(σσ)

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks