We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Arithmetic Mean

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 Next →

Example Question #31 : How To Find Arithmetic Mean

Find the arithmetic mean of the following set of numbers:

$\dpi{100} \small 6,8,12,16,18$

Possible Answers:

$\dpi{100} \small 8$

$\dpi{100} \small 16$

$\dpi{100} \small 18$

$\dpi{100} \small 6$

$\dpi{100} \small 12$

Correct answer:

$\dpi{100} \small 12$

Explanation:

The mean is adding all the numbers then dividing by the number of items.

In this case we have, $\dpi{100} \small x-b,x-y,x,x+b,x+y$

where $\dpi{100} \small x=12, b= 6, y = 4$

When this happens, the average is $\dpi{100} \small x$

Report an Error

Example Question #32 : How To Find Arithmetic Mean

$\small \textup{The average (arithmetic mean) of}\:x,\,y,\,\textup{and}\,z\,\textup{is 8.}$

$\small \textup{If}\,y=5x\,\textup{and}\,z=6,\,\textup{what is the value of}\,x?$

Possible Answers:

$\small 3$

$\small 8$

$\small 15$

$\small 5$

$\small 6$

Correct answer:

$\small 3$

Explanation:

Arithmetic mean: $\small \left ( x+y+z\right )\div3=8$ given: $\small z=6\;\;y=5x$

Solve: $\small \left ( x+5x+6\right )\div3=8$

$\small 6x+6=24$

$\small 6x=18$

$\small x=3$

Report an Error

Example Question #33 : How To Find Arithmetic Mean

A class consists of 10 students. The teacher wrote the test and expects the class to have an average score of at least 80. The average score of 9 people was calculated and it was 78. What score does the last person have to get in order to reach the teacher's standard?

Possible Answers:

$94$

$100$

$98$

$88$

$82$

Correct answer:

$98$

Explanation:

The total score of those 9 students is $9\cdot 78=702$ .

The standard score for the entire class was $10\cdot 80=800$ .

Therefore, the last person needs a score of $800-702=98$ .

Report an Error

Example Question #31 : Statistics

What is the average (mean) of

$2x+7, 3x-10, and\ -14x+12$

Possible Answers:

4x+7

-3(x+1)

3(x+1)

-3(x-1)

3(x-1)

Correct answer:

-3(x-1)

Explanation:

By adding all of the expressions we get -9x+9

which averages to -3x+3 ,

which will simplify to -3(x-1) .

Report an Error

Example Question #31 : Statistics

The mean of a series of 6 numbers (11, 12, 14, 17, 18, x) is 15. Solve for x.

Possible Answers:

Correct answer:

Explanation:

If the mean of 6 numbers is 15, that implies that the sum of the numbers is equal to 90 (6 x 15).

Therefore, $\small 90=(11+12+14+17+18+x)$ or $\small 90=(72+x)$ $\small 90-72=x=18$

Report an Error

Example Question #31 : Statistics

A police officer walked into a room full of suspects and turn out their pockets. The chart below shows the number of coins each man had.

Screen_shot_2013-09-04_at_10.20.59_am

The police claim the man with the amount of money closest to the arithmetic mean of the group is guilty. Who is it?

Possible Answers:

Suspect 2

Suspect 4

Suspect 6

Suspect 1

Suspect 3

Correct answer:

Suspect 2

Explanation:

Screen_shot_2013-09-04_at_10.26.20_am

Summing total money and dividing by the number of suspects gives us an average of approximately $2.73. By comparing it to the amounts held by the suspects, we can see that Suspect #2 is guilty.

Report an Error

Example Question #1361 : Psat Mathematics

The average temperature for 6 days in July is $87^\circ F$ . If on the seventh day, the temperature is $54^\circ F$ , what is the average temperature over those seven days?

Possible Answers:

$82.3^\circ F$

$70.5^\circ F$

$76.0^\circ F$

None of the available answers.

There is not enough information to answer this question.

Correct answer:

$82.3^\circ F$

Explanation:

In order to calculate mean, we can act as though the temperature was exactly $87^\circ F$ for the first six days and $54^\circ F$ on the seventh day. The mean can be expressed:

$\frac{(6\times 87)+54}{7}=\frac{522+54}{7}=\frac{576}{7}\approx 82.3^\circ F$

Report an Error

Example Question #34 : Statistics

If the average of $b + 2$ is equal to the average of $b + 4 + 6$ . What is the value of $b$ ?

Possible Answers:

Correct answer:

Explanation:

$\frac{b+2}{2}=\frac{b+4+6}{3}$

$3b+6=2b+8+12$

$b=14$

Report an Error

Example Question #31 : Statistics

The test average for a class of 13 students is 87%. If two students take make-up tests the next day and score 97% and 56% respectively, what is the new average?

Possible Answers:

$94.5\%$

$85.6\%$

$84.8\%$

The average does not change

$80\%$

Correct answer:

$85.6\%$

Explanation:

In order to calculate the new average, we can act as though each of the thirteen students who originally took the test each earned 87%:

$\frac{(13\times87)+97+56}{15}=85.6\%$

Report an Error

Example Question #40 : How To Find Arithmetic Mean

Tom makes a bet with his friend Bob. Bob wagers $100, but Tom decides to make him a deal. If Bob wins, Tom will pay him $100. If Tom wins, Bob will instead pay $1 for the first day, then every day for 10 days he must match the total amount paid so far.

For the first day, Bob will pay $1. The second day, he will pay an additional dollar, since he has only paid $1 thus far. The third day he will pay $2, the fourth $4, and so on.

If Bob has a 75% chance to win, which of the following is the closest to the amount of money Tom will make on average with this bet?

Possible Answers:

$\$50$

$\$25$

$\$0$

$\$ 100$

- $\$25$

Correct answer:

$\$50$

Explanation:

We are asked to find out how much Tom would win on average. Since Bob has a 75% chance to win, Tom must have a 25% chance to win. The amount Tom will lose is given to us: $100. We now need to find how much he will win.

The first day, Bob will only pay $1. Similarly for the second day. The third day Bob will now have to pay $2. The fourth day, $4. We notice that each day we will be doubling how much he pays (since he is matching how much was paid previously). Thus he is paying:

$1+2^0+2^1+2^2+2^3+2^4+...+2^{8} = 1+1+2+4+8+16+...+256$

Now, there are a couple ways to deal with this series. There are only 10 terms, so we can simply add them up to get our answer. Another method would be looking at it as a geometric series. If you recall, the sum of a geometric series (series that have terms differentiated by a constant multiplier) is given by: $a\cdot \frac{1-r^{n}}{1-r}$ where is the initial value, is the ratio between any 2 terms, and is the number of terms. Here we just have a=1 , since the first term is a 1. Each term is half the previous term, so r=2 , and we have 9 terms ( $2^{0}$ to $2^{8}$ ) so n=9 .

Hence this would be: $a \cdot \frac{1-r^{n}}{1-r}(1) = (1)\cdot \frac{1-(2)^{(9)}}{1-(2)}$

and our answer would be $1+ \frac{-511}{-1} = 1+511 = 512$

We now have that Bob will have to pay $512 if Tom wins, while Tom will have to pay $100 if Bob wins. We finally take into account the odds of winning. 25% of the time, Tom will win $512. 75% of the time he will lose $100. We can more easily interpret this with fractions: 1/4 chance to win, 3/4 chance to lose.

Now we simply keep in mind how averages work: The numerator is going to be the sum of all the cases, while the denominator is the number of cases. In this situation, we have 4 cases. 3 of them Tom loses, 1 he wins. Thus we have:

$\frac{512 - 100 - 100 - 100}{4} = \frac{512-300}{4} = \frac{212}{4} = 53$

So on average, Tom will make $53 with this bet. The closest answer to this is $50.

Report an Error

← Previous 1 2 3 4 5 6 7 8 Next →

View SAT Mathematics Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Daniel
Certified Tutor

Stony Brook University, Bachelors, Biology, General. SUNY College of Optometry, PHD, Optometry.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Miami, ISEE Courses & Classes in Houston, MCAT Courses & Classes in Boston, Spanish Courses & Classes in Miami, Spanish Courses & Classes in Philadelphia, MCAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Miami, ISEE Test Prep in Miami, GMAT Test Prep in Phoenix, SAT Test Prep in Houston, SAT Test Prep in Washington DC, ACT Test Prep in Washington DC, MCAT Test Prep in Washington DC, ISEE Test Prep in Philadelphia, GRE Test Prep in San Francisco-Bay Area

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

SAT Math : Arithmetic Mean

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #31 : How To Find Arithmetic Mean

Example Question #32 : How To Find Arithmetic Mean

Example Question #33 : How To Find Arithmetic Mean

Example Question #31 : Statistics

Example Question #31 : Statistics

Example Question #31 : Statistics

Example Question #1361 : Psat Mathematics

Example Question #34 : Statistics

Example Question #31 : Statistics

Example Question #40 : How To Find Arithmetic Mean

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: