GMAT Math : Descriptive Statistics

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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:

Statements 1 and 2 TOGETHER are NOT sufficient.

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

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

EACH statement ALONE is sufficient.

Statement 2 ALONE is sufficient, but statement 1 is 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.

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Example Question #2 : 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:

$\small .11$

$\small .02$

$\small .05$

$\small .01$

$\small .08$

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 =

$\small \small .9484$

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

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Example Question #1 : Descriptive Statistics

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

$15.68

$4.05

$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

$\small 2.066(2.1448) = 4.43$

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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:

$\small 88.1$

$\small 80.6$

$\small 84.1$

$\small 86.5$

$\small 82.8$

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.

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Example Question #5 : Dsq: Calculating Range

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:

$\small r = .4123$

$\small t = 2.66$

$\small r=.7732$

$\small t = 3.34$

$\small r = .6512$

$\small t = 2.81$

$\small r = .7125$

$\small t = 3.21$

$\small r=.5844$

$\small t = 2.22$

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 -

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

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Example Question #3 : Descriptive Statistics

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

$\small Jan=8$

$\small Feb=6$

$\small Mar=10$

$\small Apr=6$

$\small May=10$

$\small Jun=13$

$\small Jul=9$

$\small Aug=11$

$\small Sep=10$

$\small Oct=11$

$\small Nov=13$

$\small Dec=12$

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:

$\small Y=.722X + 5.5$

$\small Y=.633X + 2.1$

$\small Y=.311X + 4.2$

$\small Y=.226X + 8.1$

$\small Y=.465X + 6.9$

Correct answer:

$\small Y=.465X + 6.9$

Explanation:

Excel indicates the slope is

$\small .465$

$\small average for X = 6.5$

$\small average for Y = 9.917$

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

$\small b = 6.9$

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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).

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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:

$\small \pm7.22$

$\small \pm6.88$

$\small \pm5.20$

$\small \pm8.11$

$\small \pm6.19$

Correct answer:

$\small \pm6.19$

Explanation:

The z value for 95th percentile is:

$\small z=1.96$

the sample standard deviation is:

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

$\small 1.96(3.16)=6.19$

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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:

$\small 97$

$\small 55$

$\small 77$

$\small 67$

$\small 87$

Correct answer:

$\small 87$

Explanation:

$\small z=2.33$

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

solve for $\small n$

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Example Question #6 : 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:

$\small .50$

$\small .41$

$\small .63$

$\small .42$

$\small .37$

Correct answer:

$\small .37$

Explanation:

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

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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 #2 : Range

Example Question #1 : Descriptive Statistics

Example Question #1 : Descriptive Statistics

Example Question #5 : Dsq: Calculating Range

Example Question #3 : Descriptive Statistics

Example Question #2 : Descriptive Statistics

Example Question #8 : Dsq: Calculating Range

Example Question #9 : Dsq: Calculating Range

Example Question #6 : Dsq: Calculating Range

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