We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Statistics : Standard Deviation

Study concepts, example questions & explanations for Statistics

Create An Account

All Statistics Resources

20 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Statistics

Calculate the standard deviation of the following data set:

$3, 7, 2, 9, 8, \textup{and }10$

Possible Answers:

2.865

Cannot be determined

2.689

2.986

2.658

Correct answer:

2.986

Explanation:

The standard deviation is found by using the following formula:

$s=\sqrt{\frac{\sum \left | x-\bar{x}\right |^2}{n}}$

We will start by identifying the components of this equation:

$\sum=\textup{sum}$

$x=\textup{variable in the data set}$

$\bar{x}=\textup{mean of the data set}$

$n=\textup{total number of variables in the data set}$

Now, we can use this information to calculate the standard deviation.

First, we need to identify and $\bar{x}$ . There are six variables in the data set; therefore, we can write the following:

n=6

Next, we need to calculate the mean:

$\bar{x}=\frac{\sum x}{n}$

$\bar{x}=\frac{3+7+2+9+8+10}{6}$

$\bar{x}=\frac{39}{6}$

$\bar{x}=6.5$

Second, we need to find the square of the absolute of each variable minus the mean: $\left | x-\bar{x}\right |^2$

$\textup{For 3}=\left | 3-6.5\right |^2=12.25$

$\textup{For 7}=\left | 7-6.5\right |^2=0.25$

$\textup{For 2}=\left | 2-6.5\right |^2=20.25$

$\textup{For 9}=\left | 9-6.5\right |^2=6.25$

$\textup{For 8}=\left | 8-6.5\right |^2=2.25$

$\textup{For 10}=\left | 10-6.5\right |^2=12.25$

Last, let's substitute these values into the standard deviation formula and solve.

$s=\sqrt{\frac{\sum \left | x-\bar{x}\right |^2}{n}}$

$s=\sqrt{\frac{(12.25+0.25+20.25+6.25+2.25+12.25)}{6}}$

$s=\sqrt{\frac{53.5}{6}}$

Solve.

s=2.986

Report an Error

View Tutors

George
Certified Tutor

Pensacola State College, Bachelor in Arts, Mathematics.

View Tutors

Krittika
Certified Tutor

University of Dhaka, Master's/Graduate, Statistics. University of Waterloo, Master's/Graduate, Biostatistics.

View Tutors

Jordan
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Physics. University of Maryland-College Park, Bachelor in Arts, Ger...

All Statistics Resources

20 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in San Francisco-Bay Area, ISEE Tutors in Miami, Physics Tutors in Chicago, English Tutors in Atlanta, Computer Science Tutors in Washington DC, Biology Tutors in Denver, GRE Tutors in Denver, MCAT Tutors in Atlanta, Calculus Tutors in Chicago, MCAT Tutors in Miami

Popular Courses & Classes

MCAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Miami, ACT Courses & Classes in Phoenix, MCAT Courses & Classes in Boston, SAT Courses & Classes in Seattle, LSAT Courses & Classes in San Diego, MCAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Boston, MCAT Courses & Classes in Denver, SSAT Courses & Classes in Chicago

Popular Test Prep

SSAT Test Prep in Chicago, GMAT Test Prep in Atlanta, ISEE Test Prep in Boston, ISEE Test Prep in Los Angeles, MCAT Test Prep in Houston, ACT Test Prep in Chicago, ISEE Test Prep in Miami, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Boston, MCAT Test Prep in Philadelphia

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Statistics : Standard Deviation

Study concepts, example questions & explanations for Statistics

All Statistics Resources

Example Questions

Example Question #1 : Statistics

All Statistics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: