GMAT Math : Descriptive Statistics

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Descriptive Statistics

Calculate the average of the set of numbers.

Statement 1: the range of the set is 13

Statement 2: the mode of the set is 16

Possible Answers:

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement 2 ALONE is sufficient, but statement 1 is not sufficient.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient.

EACH statement ALONE is sufficient.

Statements 1 and 2 TOGETHER are NOT sufficient.

Correct answer:

Statements 1 and 2 TOGETHER are NOT sufficient.

Explanation:

To answer this question, we must understand the vocabulary. The range of a set is the difference between the largest and smallest numbers. The mode of a set is the number which comes up most frequently. Neither the range nor the mode, nor both, will help us solve for the average, however.

Report an Error

Example Question #1 : Dsq: Calculating Range

A high school basketball player practices 40 free throws every day. Over the past 90 days he has averaged 25 successful free throws.

What is the probability that tomorrow he will make 30 or more free throws?

Possible Answers:

$\small .05$

$\small .02$

$\small .01$

$\small .08$

$\small .11$

Correct answer:

$\small .05$

Explanation:

$\small n=40$

$\small p=.625$

$\small q=.375$

standard deviation =

$\small \sqrt{(pq)/n}=.0765$

$\small \small z=(.75-.625)/.0765=1.63$

$\small \small z=1.63$

Percentile =

$\small \small .9484$

$\small \small 1 - .9484 = .0516$

Report an Error

Example Question #1 : Range

We think that our average customer spends roughly $40 - $60 every time he/she visits our website. We can assume that the expenditure amounts are normally distributed, but, we do not know the standard deviation. We sample 15 web expenditures; our sample average is $52 and our sample standard deviation is $8.

We are 95% sure that our true population average is $52 plus or minus....

Possible Answers:

$4.43

$4.05

$15.68

$17.16

$11.56

Correct answer:

$4.43

Explanation:

standard deviation of the sample mean is:

$\small 8/\sqrt{15}=2.066$

95% $\small t$ for 14 d.o.f. =

$\small 2.1448$

confidence interval is

$\small 2.066(2.1448) = 4.43$

Report an Error

Example Question #1 : Descriptive Statistics

The average score on a statistics test is 70%. The standard deviation is 10%.

What is the minimal test score that Judy needs in order to reach the 90^th percentile?

Possible Answers:

$\small 88.1$

$\small 80.6$

$\small 82.8$

$\small 86.5$

$\small 84.1$

Correct answer:

$\small 82.8$

Explanation:

One tailed test (Z table)

$\small p=.9$

$\small z=1.28$

$\small 1.28(10)=12.8$

$\small 70+12.8=82.8$

In English - Judy must be at least 1.28 standard deviations above the average.

Report an Error

Example Question #3 : Descriptive Statistics

Our final sales figures (in millions) for the year are:

$\small Jan=8$

$\small Feb=6$

$\small Mar=10$

$\small Apr=6$

$\small May=10$

$\small Jun=13$

$\small Jul=9$

$\small Aug=11$

$\small Sep=10$

$\small Oct=11$

$\small Nov=13$

$\small Dec=12$

Use Excel to calculate the correlation coefficient between the month number

$\small Jan=1$

$\small Feb=2$

etc.

and the sales figure(s).

Also, compute the $\small t$ value for testing the confidence level for the correlation coefficient.

Possible Answers:

$\small r = .7125$

$\small t = 3.21$

$\small r=.7732$

$\small t = 3.34$

$\small r = .6512$

$\small t = 2.81$

$\small r=.5844$

$\small t = 2.22$

$\small r = .4123$

$\small t = 2.66$

Correct answer:

$\small r = .7125$

$\small t = 3.21$

Explanation:

Excel indicates the correlation coefficient $\small r$ is

$\small .7125$

$\small n-2=10$

the formula for $\small t$ is -

$\small t=r/\sqrt{(1-r^{2})/(n-2)}$

Report an Error

Example Question #2 : Descriptive Statistics

Our final sales figures (in millions) for the year are:

$\small Jan=8$

$\small Feb=6$

$\small Mar=10$

$\small Apr=6$

$\small May=10$

$\small Jun=13$

$\small Jul=9$

$\small Aug=11$

$\small Sep=10$

$\small Oct=11$

$\small Nov=13$

$\small Dec=12$

Using the above data, calculate the regression line

$\small Y=aX + b$

that best fits the data.

Hint – make the month number

$\small Jan=1$

$\small Feb=2$

etc.

the independent variable $\small X$ and make the sales figure the dependent variable $\small Y$ . Use Excel to calculate the slope.

Possible Answers:

$\small Y=.722X + 5.5$

$\small Y=.226X + 8.1$

$\small Y=.633X + 2.1$

$\small Y=.465X + 6.9$

$\small Y=.311X + 4.2$

Correct answer:

$\small Y=.465X + 6.9$

Explanation:

Excel indicates the slope is

$\small .465$

$\small average for X = 6.5$

$\small average for Y = 9.917$

$\small 9.917 = .465(6.5) + b$

$\small b = 6.9$

Report an Error

Example Question #2 : Descriptive Statistics

The average sales price of a home in Ourtown U.S.A. is $120,000.

The population standard deviation is $20,000.

What is the probability that the next home will sell for more than $130,000?

Possible Answers:

$\small .28$

$\small .31$

$\small .42$

$\small .77$

$\small .69$

Correct answer:

$\small .31$

Explanation:

$\small (130-120)/20=.5$

$\small .5$ translates to:

$\small .6915$ percentile (below) and

$\small .3085$ percentile (above).

Report an Error

Example Question #8 : Dsq: Calculating Range

We are trying to determine the average age of the Cardinal baseball fan. We know that the age distribution of Cardinal nation is normally distributed with a standard deviation of 20. We need to determine the average age. We take a sample of 40 fans and the average of our sample is 42 years old.

What is the 95% confidence interval (range) for our sample average of 42? (remember – confidence intervals are always 2- tailed (plus or minus)).

Possible Answers:

$\small \pm6.88$

$\small \pm8.11$

$\small \pm6.19$

$\small \pm7.22$

$\small \pm5.20$

Correct answer:

$\small \pm6.19$

Explanation:

The z value for 95th percentile is:

$\small z=1.96$

the sample standard deviation is:

$\small 20/ \sqrt{40}) = 3.16$

$\small 1.96(3.16)=6.19$

Report an Error

Example Question #9 : Dsq: Calculating Range

However, the Cardinal President of Operations wants a 98% confidence interval of plus or minus 5.0. What sample size do we need to satisfy his request?

Possible Answers:

$\small 97$

$\small 87$

$\small 67$

$\small 77$

$\small 55$

Correct answer:

$\small 87$

Explanation:

$\small z=2.33$

$\small \small 5=2.33(20/ \sqrt{n})$

solve for $\small n$

Report an Error

Example Question #7 : Dsq: Calculating Range

The Cardinals average 4 extra inning games per month.

What is the probability that they will have more than 4 extra inning games next month? Hint – Poisson distribution.

Possible Answers:

$\small .41$

$\small .37$

$\small .63$

$\small .50$

$\small .42$

Correct answer:

$\small .37$

Explanation:

$\small .37=1-P\left [ 0\right ]-P\left [ 1\right ]-P\left [ 2\right ]-P\left [ 3\right ]-P\left [ 4\right ]$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Los Angeles, SSAT Tutors in Seattle, Computer Science Tutors in Houston, SSAT Tutors in Dallas Fort Worth, LSAT Tutors in Washington DC, Chemistry Tutors in Philadelphia, SSAT Tutors in Houston, Computer Science Tutors in Los Angeles, SAT Tutors in Washington DC, French Tutors in Chicago

Popular Courses & Classes

Spanish Courses & Classes in Boston, LSAT Courses & Classes in Chicago, SSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Boston, MCAT Courses & Classes in Atlanta, GRE Courses & Classes in Los Angeles, SSAT Courses & Classes in Seattle, ACT Courses & Classes in Boston, Spanish Courses & Classes in Philadelphia, GRE Courses & Classes in Philadelphia

Popular Test Prep

ACT Test Prep in Boston, GMAT Test Prep in Chicago, GMAT Test Prep in Philadelphia, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in San Diego, GMAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Seattle, LSAT Test Prep in Phoenix, SSAT Test Prep in Houston, ISEE Test Prep in New York City

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)

Email address:
Your name:
Feedback:

GMAT Math : Descriptive Statistics

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Descriptive Statistics

Example Question #1 : Dsq: Calculating Range

Example Question #1 : Range

Example Question #1 : Descriptive Statistics

Example Question #3 : Descriptive Statistics

Example Question #2 : Descriptive Statistics

Example Question #2 : Descriptive Statistics

Example Question #8 : Dsq: Calculating Range

Example Question #9 : Dsq: Calculating Range

Example Question #7 : Dsq: Calculating Range

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details