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 #1 : How To Find Standard Deviation

Find the standard deviation of the following set of numbers: 10, 15, 19, 35, 27, 44. Round your answer to the nearest tenth.

Possible Answers:

11.7

137.7

Correct answer:

11.7

Explanation:

To find the standard deviation of a set of numbers, first find the mean (average) of the set of numbers:

$\frac{10+15+19+35+27+44}{6}=25$

Second, for each number in the set, subtract the mean and square the result:

(10-25)^2+(15-25)^2+(19-25)^2+(35-25)^2 +(27-25)^2+(44-25)^2=826

Then add all of the squares together and find the mean (average) of the squares, like this:

$\frac{826}{6}=137.67$

Finally, take the square root of the second mean:

$\sqrt{137.7}=11.7$ .

Report an Error

Example Question #1 : How To Find Standard Deviation

Find the standard deviation of the following set of numbers: 10, 15, 7, 13. Round your answer to the nearest hundredth.

Possible Answers:

1.56

3.06

11.25

9.19

3.03

Correct answer:

3.03

Explanation:

To find the standard deviation of a set of numbers, first find the mean (average) of the set of numbers:

$\frac{110+15+7+13}{4}=11.25$

Second, for each number in the set, subtract the mean and square the result:

(10-11.25)^2+(15-11.25)^2+(7-11.25)^2+(13-11.25)^2=36.74

Then add all of the squares together and find the mean (average) of the squares, like this:

$\frac{36.74}{4}=9.19$

Finally, take the square root of the second mean: $\sqrt{9.19}=3.03$ .

Report an Error

Example Question #1 : How To Find Standard Deviation

Kyle scored the following on his mathematics tests: 60, 75, 80, 75, 70 . What is the standard deviation of his test scores? Round your answer to the nearest tenth.

Possible Answers:

212

42.4

6.8

Correct answer:

6.8

Explanation:

To find the standard deviation of a set of numbers, first find the mean (average) of the set of numbers:

$\frac{60+75+80+75+70}{5}=72$

Second, for each number in the set, subtract the mean and square the result:

(60-72)^2+(75-72)^2+(80-72)^2+(75-72)^2 +(70-72)^2=230 .

Then add all of the squares together and find the mean (average) of the squares, like this:

$\frac{230}{5}=46$

Finally, take the square root of the second mean:

$\sqrt{46}=6.8$ .

Report an Error

Example Question #1 : How To Find Standard Deviation

Mr. Bell gave out a science test last week to six honors students. The scores were 88, 94, 80, 79, 74, and 83. What is the standard deviation of the scores? (Round to the nearest tenth.)

Possible Answers:

81.5

6.5

Correct answer:

6.5

Explanation:

First, find the mean of the six numbers by adding them all together, and dividing them by six.

88 + 94 + 80 + 79 + 74 + 83 = 498

498/6 = 83

Next, find the variance by subtracting the mean from each of the given numbers and then squaring the answers.

88 – 83 = 5

5² = 25

94 – 83 = 11

11² = 121

80 – 83 = –3

–3² = 9

79 – 83 = –4

–4² = 16

74 – 83 = –9

–9² = 81

83 – 83 = 0

0² = 0

Find the average of the squared answers by adding up all of the squared answers and dividing by six.

25 + 121 + 9 +16 +81 + 0 = 252

252/6 = 42

42 is the variance.

To find the standard deviation, take the square root of the variance.

The square root of 42 is 6.481.

Report an Error

Example Question #1 : How To Find Standard Deviation

Give the interquartile range of a data set with the following characteristics.

Mean: 72.1

Median: 70

Standard deviation: 4.6

Possible Answers:

4.2

8.4

9.2

18.4

It cannot be determined from the information given.

Correct answer:

It cannot be determined from the information given.

Explanation:

The interquartile range is the difference between the first and third quartiles. The two pieces of information needed to determine interquartile range, the first and third quartiles, are missing; therefore, it is impossible to answer the question without more information.

Report an Error

Example Question #41 : Statistical Concepts

On his five tests for the semester, Andrew earned the following scores: 83, 75, 90, 92, and 85. What is the standard deviation of Andrew's scores? Round your answer to the nearest hundredth.

Possible Answers:

5.97

5.98

5.95

5.93

Correct answer:

5.97

Explanation:

The following is the formula for standard deviation:

$s = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}$

Here is a breakdown of what that formula is telling you to do:

1. Solve for the mean (average) of the five test scores
2. Subtract that mean from each of the five original test scores. Square each of the differences.
3. Find the mean (average) of each of these differences you found in Step 2
4. Take the square root of this final mean from #3. This is the standard deviation

Here are those steps:

1. Find the mean of the test scores:

$(83+75+90+92+85) \div 5 = 425 \div 5 = 85$

2. Subtract the mean from each of the test scores, then square the differences:

83-85 = (-2)^2 = 4

75-85 = (-10)^2 = 100

90-85 = (5)^2 = 25

92-85 = (7)^2 = 49

85-85 = (0)^2 = 0

3. Find the mean of the squared values from Step 2:

$(4+100+25+49+0) \div5 = 178\div 5= 35.6$

4. Take the square root of your answer from Step 3:

$\sqrt{35.6} = 5.9667 = 5.97$

Report an Error

Example Question #2 : How To Find Standard Deviation

In her last six basketball games, Jane scored 15, 17, 12, 15, 18, and 22 points per game. What is the standard deviation of these score totals? Round your answer to the nearest tenth.

Possible Answers:

3.1

3.0

3.2

3.3

Correct answer:

3.1

Explanation:

The following is the formula for standard deviation:

$s = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}$

Here is a breakdown of what that formula is telling you to do:

Here are those steps:

1. Find the mean of her score totals:

$(15+17+12+15+18+22) \div 6 = 99 \div 6 =16.5$

2. Subtract the mean from each of the test scores, then square the differences:

15-16.5 = (-1.5)^2 = 2.25

17-16.5 = (0.5)^2 = 0.25

12-16.5 = (-4.5)^2 = 20.25

15-16.5 = (-1.5)^2 = 2.25

18-16.5 = (1.5)^2 = 2.25

22-16.5 = (5.5)^2 = 30.25

3. Find the mean of the squared values from Step 2:

$(2.25+0.25+20.25+2.25+2.25+30.25) \div6 =$

$57.5\div 6= 9.58\bar{3}$

4. Take the square root of your answer from Step 3:

$\sqrt{9.58\bar{3}} = 3.096 = 3.1$

Report an Error

Example Question #1 : How To Find Standard Deviation

The variance is . What is the standard deviation?

Possible Answers:

7.483

7.682

3136

9.985

Correct answer:

7.483

Explanation:

Write the formula for standard deviation in terms of variance.

$\sigma=\sqrt{V}$

Substitute the variance.

$\sigma=\sqrt{56}= 7.483$

Report an Error

Example Question #1 : How To Find Standard Deviation

In meteorology, the standard deviation of wind speed can be used to predict the likelihood of fog forming under given temperature conditions.

What is the standard deviation of the following wind speed measurements in kilometers per hour (kph), taken 1 hour apart at the same site for 10 hours? Round to the nearest tenth.

6, 4, 13, 11, 8, 6, 4, 5, 7, 7

Possible Answers:

23.2

50.41

2.9

85.3

3.1

Correct answer:

2.9

Explanation:

The first step in calculating standard deviation, or $\sigma$ , is to calculate the mean for your sample, or $\mu$ . Remember, to calculate mean, sum your data values and divide by the count, or number of values you have.

$\mu= \frac{x_{1} +x_{2} + ...x_{n}}{n} = \frac{6+4+13+11+8+6+4+5+7+7}{10} = 7.1$

Next, we must find the difference between each recorded value and the mean. At the same time, we will square these differences, so it does not matter whether you subtract the mean from the value or vice versa.

We use $\sum_{i=1}^{N} (x_{i}-\mu)^{2}$ to represent this, but all it really means is that you square the difference between each value $x_{i}$ , where is the position of the value you're working with, and the mean, $\mu$ . Then we sum all those differences up (the part that goes $\sum_{i=1}^{N}$ , where is your count. i=1 just refers to the fact that you start at the first value, so you include them all.)

It's probably easier to do than to think about at first, so let's dive in!

$(6-7.1)^{2} = 1.21$

$(4-7.1)^{2} = 9.61$

$(13-7.1)^{2} = 34.81$

$(11-7.1)^{2} = 15.21$

$(8-7.1)^{2} = .81$

$(6-7.1)^{2} = 1.21$

$(4-7.1)^{2} = 9.61$

$(5-7.1)^{2} = 4.41$

$(7-7.1)^{2} = .01$

$(10-7.1)^{2} = 8.41$

Now, add the deviations, and we're nearly there!

$\sum_{i=1}^{N} (x_{i}-\mu)^{2} = 1.21 + 6.91 + 34.81 + ... + 8.41 = 85.29$

Next, we must divide this number by our :

$\frac{85.29}{N} = 8.529$

This number, 8.529, is our variance, or $\sigma^{2}$ . Since standard variation is $\sigma$ , you may have guessed what we must do next. We must take the square root of the summed squares of deviations.

$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_{i}-\mu)^{2}} = \sqrt{8.529} = 2.92$

So, our standard deviation is 2.9 kph (remembering the problem told us to round to 1 decimal point.)

Report an Error

Example Question #1 : How To Find Standard Deviation

Actuaries (people who determine insurance premiums for things like life and car insurance) often have to look at the average insurance costs in an area. One way to do this without letting outliers affect their data is to take the standard deviation of insurance costs in an area over a given period of time.

Calculate the standard deviation from the data set of insurance claims for a region over one-year periods (units in millions of dollars). Round your final answer to the nearest million dollars.

32, 38, 16, 21, 25, 28, 23, 31, 16, 25, 32

Possible Answers:

Correct answer:

Explanation:

$\mu= \frac{x_{1} +x_{2} + ...x_{n}}{n} = \frac{32+38+16+21+25+28+23+31+16+25+32}{11} \approx 26.1$

We use $\sum_{i=1}^{N} (x_{i}-\mu)^{2}$ to represent this, but all it really means is that you square the difference between each value $x_{i}$ , where is the position of the value you're working with, and the mean, $\mu$ . Then we sum all those differences up (the part that goes $\sum_{i=1}^{N}$ , where is your count. $_{i=1}$ just refers to the fact that you start at the first value, so you include them all.)

It's probably easier to do than to think about at first, so let's dive in!

$(32-26.1)^{2} = 34.81$

$(38-26.1)^{2} = 141.61$

$(16-26.1)^{2} = 102.01$

$(21-26.1)^{2} = 26.01$

(25-26.1)^2 = 1.21

$(28-26.1)^{2} = 3.61$

$(23-26.1)^{2} = 9.61$

$(31-26.1)^{2} = 24.01$

$(16-26.1)^{2} = 102.01$

(25-26.1)^2 = 1.21

$(32-26.1)^{2} = 34.81$

Now, add the deviations, and we're nearly there!

$\sum_{i=1}^{N} (x_{i}-\mu)^{2} = 34.81 + 141.61 + 102.01 + ... + 34.81 = 480.9$

Next, we must divide this number by our :

$\frac{480.9}{11} = 43.72$

This number, 43.35, is our variance, or $\sigma^{2}$ . Since standard variation is $\sigma$ , you may have guessed what we must do next. We must take the square root of the summed squares of deviations.

$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_{i}-\mu)^{2}} = \sqrt{43.72} = 6.612$

So, our standard deviation is 7 million dollars (remembering to round to the nearest million, per our instructions.)

Report an Error

View Algebra Tutors

Hayley
Certified Tutor

University of North Florida, Bachelor in Arts, English.

View Algebra Tutors

Carolyn
Certified Tutor

University of California-Los Angeles, Bachelor in Arts, Mathematics.

View Algebra Tutors

Mykalin
Certified Tutor

Worcester Polytechnic Institute, Bachelor of Science, Astrophysics. Worcester Polytechnic Institute, Master of Science, Nucle...

All Algebra 1 Resources

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

Popular Subjects

Statistics Tutors in Boston, Biology Tutors in Washington DC, GMAT Tutors in Miami, MCAT Tutors in Chicago, GMAT Tutors in New York City, ISEE Tutors in Atlanta, MCAT Tutors in Los Angeles, Math Tutors in Seattle, Chemistry Tutors in Phoenix, ACT Tutors in Chicago

Popular Courses & Classes

SSAT Courses & Classes in San Diego, SSAT Courses & Classes in Chicago, LSAT Courses & Classes in Atlanta, SSAT Courses & Classes in Los Angeles, Spanish Courses & Classes in San Diego, ISEE Courses & Classes in Boston, GRE Courses & Classes in Phoenix, MCAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Washington DC

Popular Test Prep

SAT Test Prep in Los Angeles, SSAT Test Prep in San Diego, SSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in New York City, ACT Test Prep in Houston, LSAT Test Prep in Chicago, SAT Test Prep in Miami, GMAT Test Prep in Boston, GRE Test Prep in Phoenix, ISEE Test Prep in Houston

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 #1 : How To Find Standard Deviation

Example Question #1 : How To Find Standard Deviation

Example Question #1 : How To Find Standard Deviation

Example Question #1 : How To Find Standard Deviation

Example Question #1 : How To Find Standard Deviation

Example Question #41 : Statistical Concepts

Example Question #2 : How To Find Standard Deviation

Example Question #1 : How To Find Standard Deviation

Example Question #1 : How To Find Standard Deviation

Example Question #1 : 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: