We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Variance

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Variance

Calculate the variance of the following set of values.

$\left \{ 3,3,4,5,8,7\right \}$

Possible Answers:

3.67

1.91

1.67

Correct answer:

3.67

Explanation:

Variance is the average of the squared differences from the mean. So start by working out the mean of the set of values.

$\frac{(3+3+4+5+8+7)}{6}=5$

Then, for each number, subtract the mean and square the result.

$(3-5)^{2}=(-2)^{2}=4$

$(4-5)^{2}=(-1)^{2}=1$

$(5-5)^{2}=(0)^{2}=0$

$(8-5)^{2}=(3)^{2}=9$

$(7-5)^{2}=(2)^{2}=4$

The average of the results is the variance.

$\frac{(4+4+1+0+9+4)}{6}=3.67$

Report an Error

Example Question #2 : Variance

What is the variance of the following set of numbers?

(17,13,21,14,10)

Possible Answers:

$2\sqrt{6}$

$5\sqrt{3}$

Correct answer:

Explanation:

Remember that the variance of a set of numbers is equal to its standard deviation squared. So if the formula for standard deviation is known to be:

$\sigma =\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i-\mu )^2}$

Then the variance is simply $\sigma^2$ , given by the following equation:

$\sigma^2 =\frac{1}{N}\sum_{i=1}^{N}(x_i-\mu )^2$

Where $\sigma^2$ is the variance, N is the number of values in the set, x_i is the number currently being evaluated in the summation, and $\mu$ is the mean of the set. So all we must do to find the variance is determine our mean, and then sum the values given by subtracting the mean from each number in the set and squaring it, dividing the final sum by N to give us our variance. We start by determining the mean of the set:

$\mu=\frac{\sum_{i=1}^{N}x_i}{N}=\frac{17+13+21+14+10}{5}=15$

We then find each value that will be added together by subtracting our mean from each of the numbers in our set and then squaring the result:

(17-15)^2=4

(13-15)^2=4

(21-15)^2=36

(14-15)^2=1

(10-15)^2=25

Looking at our formula for variance, all we must do now is add these values together and divide by N:

$\sigma^2 =\frac{1}{5}(4+4+36+1+25)=14$

Report an Error

Example Question #1 : Deviation Concepts

A set of five numbers is given as follows, where one of the numbers, , is unknown:

(37,42,39,33,x)

If the mean of the set is , what is the variance?

Possible Answers:

28.8

31.6

35.4

24.7

19.9

Correct answer:

28.8

Explanation:

Before we can determine the variance of the set, we must first determine the value of x, our unknown. The problem tells us the mean of the set, and we know each number in the set except for x, so we can solve for x as follows:

$\mu =\frac{\sum_{i=1}^{N}x_i}{N}=\frac{37+42+39+33+x}{5}=40$

$151+x=200\rightarrow x=49$

Now that we know all the values of the set, the mean, and the number of values, we can solve for the variance using the following equation:

$\sigma ^2=\frac{1}{N}\sum_{i=1}^{N}(x_i-\mu )^2$

Where $\sigma ^2$ is the variance, N is the number of values in the set, x_i is the value currently being evaluated in the set, and $\mu$ is the mean of the set. We start by determing the value of each term in the summation part of the formula:

(37-40)^2=9

(42-40)^2=4

(39-40)^2=1

(33-40)^2=49

(49-40)^2=81

Now that we now each value of the summation, all we have left to do is add them all together and divide the final result by N:

$\sigma ^2=\frac{1}{5}(9+4+1+49+81)=\frac{144}{5}=28.8$

Report an Error

Example Question #4 : Variance

What is the variance for the values , , and ?

Possible Answers:

$\frac{2}{9}$

$\frac{2}{3}$

$\frac{4}{5}$

$\frac{3}{2}$

Correct answer:

$\frac{2}{3}$

Explanation:

Write the formula for variance.

$\sigma^2 = \frac{\sum (X-\mu)^2 }{N}$

The value of represents each number in the data set.

The value of is 3, since there are 3 numbers in the data set.

Find the mean, $\mu$ .

$\mu= \frac{2+3+4}{3} = \frac{9}{3}=3$

Rewrite the variance formula:

$\sigma^2 = \frac{(2-3)^2 +(3-3)^2+(4-3)^2}{3} = \frac{1+0+1}{3}=\frac{2}{3}$

Report an Error

Example Question #5 : Variance

Determine the variance if the standard deviation is 8.6 .

Possible Answers:

2.93

73.70

2.15

73.96

25.22

Correct answer:

73.96

Explanation:

Write the formula relationship between standard deviation and variance.

The standard deviation is the square root of variance.

$\sigma = \sqrt{\textup{Variance}}$

Substitute the standard deviation.

$8.6 = \sqrt{\textup{Variance}}$

Square both sides.

$\textup{Variance} =( 8.6)^2 = 73.96$

The answer is: 73.96

Report an Error

Example Question #6 : Variance

Evaluate the variance if the standard deviation is 19.5 .

Possible Answers:

7414.875

380.25

1.29

4.416

2.692

Correct answer:

380.25

Explanation:

Write the formula for the variance.

$\textup{Variance} =\sigma^2$

$\textup{Standard Deviation}= \sigma$

The standard deviation is the square root of variance.

$\sigma = \sqrt{\textup{Variance}}$

Substitute the value of standard deviation in the formula.

$19.5 = \sqrt{\textup{Variance}}$

Square both sides.

$\textup{Variance }= 380.25$

The answer is: 380.25

Report an Error

Example Question #7 : Variance

The standard deviation of a distribution is 9. What is the variance?

Possible Answers:

Correct answer:

Explanation:

The variance of a distribution is equal to the standard deviation squared.

9^2=81

Report an Error

Example Question #8 : Variance

Determine the population variance given the following data set: [5,7,27]

Possible Answers:

$\frac{296}{3}$

148

280

Correct answer:

$\frac{296}{3}$

Explanation:

To determine the variance, we will need to find the squared differences of the mean, and take the average.

Find the mean.

$\frac{5+7+27}{3} = \frac{39}{3}=13$

Subtract each number from the mean and square the quantities.

(5-13)^2+(7-13)^2+(27-13)^2 = 64+36+196 = 296

Divide this value by three.

The answer is: $\frac{296}{3}$

Report an Error

View Algebra 2 Tutors

Emilie
Certified Tutor

Western Governors University, Bachelor of Science, Accounting and Business Management. Western Governors University, Master o...

View Algebra 2 Tutors

Archana
Certified Tutor

Texas A & M University-College Station, Master of Science, Mathematics.

View Algebra 2 Tutors

Dana
Certified Tutor

Northern Arizona University, Bachelor in Arts, Law Enforcement Intelligence Analysis. Grand Canyon University, Master of Scie...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Philadelphia, GRE Tutors in Atlanta, GMAT Tutors in San Francisco-Bay Area, ISEE Tutors in Chicago, Computer Science Tutors in Washington DC, LSAT Tutors in Los Angeles, Math Tutors in Washington DC, SAT Tutors in Los Angeles, ACT Tutors in New York City, ACT Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Philadelphia, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Miami, SAT Courses & Classes in Miami, GRE Courses & Classes in San Diego, SAT Courses & Classes in Phoenix, SSAT Courses & Classes in Houston, Spanish Courses & Classes in Atlanta, MCAT Courses & Classes in Houston, ACT Courses & Classes in Atlanta

Popular Test Prep

SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Los Angeles, ACT Test Prep in Miami, GMAT Test Prep in Chicago, GMAT Test Prep in Phoenix, ACT Test Prep in New York City, SAT Test Prep in Los Angeles, ACT Test Prep in Seattle, ISEE Test Prep in Houston, GMAT Test Prep in Denver

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

Algebra II : Variance

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Variance

Example Question #2 : Variance

Example Question #1 : Deviation Concepts

Example Question #4 : Variance

Example Question #5 : Variance

Example Question #6 : Variance

Example Question #7 : Variance

Example Question #8 : Variance

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: