We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to find standard deviation

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : How To Find Standard Deviation

Find the standard deviation of the data set: (1,3,8)

Possible Answers:

5.635

8.667

1.872

2.483

2.944

Correct answer:

2.944

Explanation:

Write the formula of standard deviation.

$\sigma=\sqrt{\frac{1}{N}\sum_{a=1}^{N}(x_a-\mu)^2}= \sqrt{\textup{Variance}}$

Determine the mean, $\mu$ .

$\mu=\frac{1+3+8}{3}= \frac{12}{3}= 4$

Subtract each number in the dataset from the mean and square each result.

This is the $x_a-\mu$ term.

(1-4)^2= (-3)^2=9

(3-4)^2= (-1)^2=1

(8-4)^2= (4)^2=16

Find the mean of the squared differences, or the variance.

This is the $\frac{1}{N}\sum_{a=1}^{N}(x_a-\mu)^2$ term.

$\textup{Variance}= \frac{9+1+16}{3}=\frac{26}{3}$

Square root the variance for the standard deviation.

$\sigma=\sqrt{\frac{26}{3}}= 2.944$

Report an Error

Example Question #1991 : Algebra 1

Find the standard deviation. Round your answer to the nearest tenth.

1, 3, 5, 7, 9

Possible Answers:

2.8

4.8

1.6

4.6

Correct answer:

2.8

Explanation:

To find standard deviation, we apply this formula: $\sqrt{\frac{1}{n}\Sigma (\bar{x}-x)^2}$ .

n represents how many data in the set.

$\bar{x}$ represents the average of the data in the set.

is any data in the set.

$\Sigma$ is summation of the difference between average and any data value squared.

So the mean is $\frac{1+3+5+7+9}{5}=5$ . Now, we apply the formula.

$\sqrt{\frac{1}{5}[(5-1)^2+(5-3)^2+(5-5)^2+(5-7)^2+(5-9)^2]}}$

$=\sqrt{\frac{1}{5}[16+4+0+4+16])}$

$=\sqrt{\frac{1}{5}(40)}$

=2.8

Report an Error

Example Question #13 : How To Find Standard Deviation

Find the standard deviation. Round your answer to the nearest tenth.

3, 6, 9, 12, 15

Possible Answers:

4.2

4.7

7.5

Correct answer:

4.2

Explanation:

To find standard deviation, we apply this formula: $\sqrt{\frac{1}{n}\Sigma (\bar{x}-x)^2}$ .

n represents how many data in the set.

$\bar{x}$ represents the average of the data in the set.

is any data in the set.

$\Sigma$ is summation of the difference between average and any data value squared.

So the mean is $\frac{3+6+9+12+15}{5}=9$ . Now, we apply the formula.

$\sqrt{\frac{1}{5}[(9-3)^2+(9-6)^2+(9-9)^2+(9-12)^2+(9-15)^2]}}$

$=\sqrt{\frac{1}{5}[36+9+0+9+36])}$

$=\sqrt{\frac{1}{5}(90)}$

=4.2

Report an Error

Example Question #1992 : Algebra 1

Find the standard deviation of the following set of numbers:

7, 10, 13

Possible Answers:

$\sqrt{6}$

$\sqrt{7}$

$\sqrt{10}$

Correct answer:

$\sqrt{6}$

Explanation:

To find standard deviation, we will follow these steps:

Find the mean of the original set of numbers.
Subtract the mean from each of the original numbers.
Square each number.
Find the mean of the new set of numbers.
Take the square root of the mean.

So, we will take this step by step.

STEP 1

$\text{mean} = \frac{7 + 10 + 13}{3}$

$\text{mean} = \frac{30}{3}$

$\text{mean} = 10$

STEP 2

7, 10, 13

(7-10), (10-10), (13-10)

-3, 0, 3

STEP 3

(-3)^2, 0^2, 3^2

9, 0, 9

STEP 4

$\text{mean} = \frac{9+0+9}{3}$

$\text{mean} = \frac{18}{3}$

$\text{mean} = 6$

STEP 5

$\sqrt{6}$

Thefore, the standard deviation is $\sqrt{6}$ .

Report an Error

Example Question #15 : How To Find Standard Deviation

Find the standard deviation of the following set of numbers:

1,3,4,7,10,13,16,17,19

Possible Answers:

$5\sqrt{14}$

$\sqrt{43.75}$

Correct answer:

$5\sqrt{14}$

Explanation:

To solve, you must use the following equation:

$\sigma=\sqrt{\frac{\sum_{1}^{i}(x_{i}-x_{m})^2}{n-1}}$

where,

$mean=x_{m}$

Thus,

$\sigma = \sqrt{\frac{(1-10)^2+(3-10)^2+(4-10)^2+(7-10)^2+(10-10)^2+(13-10)^2+(16-10)^2+(17-10)^2+(19-10)^2}{8}}$

$\\ \sigma = \sqrt{\frac{81+49+36+9+0+9+26+49+81}{8}}=\sqrt{\frac{350}{8}}=\sqrt{43.75} \approx 6.614$

Report an Error

Example Question #16 : How To Find Standard Deviation

Find the standard deviation of the following set of numbers.

1,4,5,5,6,15,15,16,23

Possible Answers:

$\frac{\sqrt{438}}{3}$

$\sqrt{438}$

Correct answer:

$\frac{\sqrt{438}}{3}$

Explanation:

To solve, simply use the formula for standard deviation. Thus,

$\sigma =\sqrt{\frac{\sum_{i=1}^{n}(x_i-x_m)^2}{n}}$ where xm is the mean. Thus,

$\sigma =\sqrt{\frac{(1-10)^2+(4-10)^2+(5-10)^2+(5-10)^2+(6-10)^2+(15-10)^2+(15-10)^2+(16-10)^2+(23-10)^2}{9}}$

$\sigma =\sqrt{\frac{9^2+6^2+5^2+5^2+4^2+5^2+5^2+6^2+13^2}{9}}=\sqrt{\frac{438}{9}}=\frac{\sqrt{438}}{3}$

Report an Error

Example Question #11 : How To Find Standard Deviation

Find the standard deviation of the following data set:

4, 2, 6, 8, 8, 2, 8, 10, 6.

Possible Answers:

Correct answer:

Explanation:

To find the standard deviation, we will go through a few steps.

Step 1: Find the mean.

We will find the mean of the data set.

$\text{mean} = \frac{4+2+6+8+8+2+8+10+6}{9}$

$\text{mean} = \frac{54}{9}$

$\text{mean} = 6$

Step 2: Subtract the mean from each number in the data set.

We will now take each number in the data set and subtract the mean from it.

4 - 6 = -2

2 - 6 = -4

6 - 6 = 0

8 - 6 = 2

2 - 6 = -4

8 - 6 = 2

10 - 6 = 4

6 - 6 = 0

Giving us a new data set of -2, -4, 0, 2, 2, -4, 2, 4, 0.

Step 3: Square each number in the data set.

(-2)^2 = 4

(-4)^2 = 16

0^2 = 0

2^2 = 4

(-4)^2= 16

2^2 = 4

4^2 = 16

0^2 = 0

Giving us a new data set of 4, 16, 0, 4, 4, 16, 4, 16, 0.

Step 4: Add each number in the data set together.

4 + 16 + 0 + 4 + 4 + 16 + 4 + 16 + 0 = 64

Giving us an answer of 64.

Step 5: Take the square root of the answer.

$\sqrt{64} = 8$

That is the standard deviation! So, the standard deviation of the data set

4, 2, 6, 8, 8, 2, 8, 10, 6

is 8.

Report an Error

Example Question #11 : How To Find Standard Deviation

If the variance of a set of sample data is 100 , what is the standard deviation?

Possible Answers:

3.5

5.5

12.5

Correct answer:

Explanation:

The formula for finding the standard deviation given the variance is:

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

Substitute the variance.

$SD = \sqrt{100}=10$

The standard deviation is .

Report an Error

Example Question #571 : Statistics And Probability

Approximate the standard deviation of the given set of numbers to three decimal places: [1, 2, 9]

Possible Answers:

3.559

4.136

4.742

3.874

3.426

Correct answer:

3.559

Explanation:

Write the formula for standard deviation.

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

represents the total numbers in the data set: N=3

$\mu$ is the mean: $\mu = \frac{1+2+9}{3} =\frac{12}{3} = 4$

Find the mean of the squared differences. Subtract each number in the data set with the mean, square the quantities, and take the average.

This will be the variance:

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

$\frac{1}{3} \cdot [ (9-4)^2+(2-4)^2+(1-4)^2]$

$\frac{1}{3} \cdot [ (5)^2+(-2)^2+(-3)^2] = \frac{1}{3}[25+4+9]= \frac{38}{3}$

The standard deviation is the square root of the variance, which is the square root of this fraction.

$\sqrt{\frac{38}{3}} = 3.559$

The answer is: 3.559

Report an Error

Example Question #11 : How To Find Standard Deviation

If the variance of a data set is 60, what must be the standard deviation? Round to three decimal places.

Possible Answers:

6.372

7.746

8.532

7.328

7.546

Correct answer:

7.746

Explanation:

The standard deviation is the square root of variance.

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

Substitute the variance.

$\sigma = \sqrt{\textup{60}} = 7.746$

The answer is: 7.746

Report an Error

View Algebra Tutors

Mohammad
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Mathematics. Rutgers University-New Brunswick, Master of Science, Stat...

View Algebra Tutors

Jason
Certified Tutor

Brigham Young University, Bachelor, Neuroscience.

View Algebra Tutors

Alvin
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Computer Science.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Philadelphia, Algebra Tutors in Chicago, Chemistry Tutors in Denver, SAT Tutors in San Diego, English Tutors in Chicago, Statistics Tutors in Atlanta, ACT Tutors in Phoenix, ACT Tutors in Seattle, Spanish Tutors in Houston, Reading Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in New York City, GMAT Courses & Classes in Boston, SSAT Courses & Classes in Boston, GRE Courses & Classes in New York City, SAT Courses & Classes in Houston, SAT Courses & Classes in Chicago, SSAT Courses & Classes in Denver, SSAT Courses & Classes in Miami, GRE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in New York City, ISEE Test Prep in Houston, ACT Test Prep in Philadelphia, GMAT Test Prep in Atlanta, SAT Test Prep in Chicago, SSAT Test Prep in Miami, GMAT Test Prep in Boston, MCAT 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 1 : How to find standard deviation

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : How To Find Standard Deviation

Example Question #1991 : Algebra 1

Example Question #13 : How To Find Standard Deviation

Example Question #1992 : Algebra 1

STEP 1

STEP 2

STEP 3

STEP 4

STEP 5

Example Question #15 : How To Find Standard Deviation

Example Question #16 : How To Find Standard Deviation

Example Question #11 : How To Find Standard Deviation

Step 1: Find the mean.

Step 2: Subtract the mean from each number in the data set.

Step 3: Square each number in the data set.

Step 4: Add each number in the data set together.

Step 5: Take the square root of the answer.

Example Question #11 : How To Find Standard Deviation

Example Question #571 : Statistics And Probability

Example Question #11 : How To Find Standard Deviation

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: