GMAT Math : Descriptive Statistics

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Example Questions

Example Question #463 : Arithmetic

Find the range of the following set of numbers:

$\textup{4,6,7,7,8,10,28}$

Possible Answers:

Correct answer:

Explanation:

To find range, subtract the smallest number from the largest number. Thus,

$\textup{range}=28-4=24$

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Example Question #11 : Descriptive Statistics

Find the range of the following set of numbers.

1,1,2,7,8,10,11

Possible Answers:

Correct answer:

Explanation:

To find the range, you m ust subtract the smallest number from the largest. Thus,

11-1=10

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Example Question #465 : Arithmetic

Find the range of the following data set:

89,34,117,42,367,2,989,463,865

Possible Answers:

444.5

987

989

Correct answer:

987

Explanation:

Find the range of the following data set:

89,34,117,42,367,2,989,463,865

Range is as simple as finding the diffference between the largest and smallest terms in a set. So, let's find our largest and smallest terms.

Largest: 989

Smallest: 2

Next, let's calculate the range:

r=989-2=987

So our answer should be 987

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Example Question #14 : Descriptive Statistics

A = B > C > D = E > F .

Give the midrange of the set $\left \{ A, B, C, D, E,F\right \}$ .

Possible Answers:

$\frac{A+F}{2}$

$\frac{A +B+ C+D+E+F }{6}$

$\frac{C+D}{2}$

Correct answer:

$\frac{A+F}{2}$

Explanation:

The midrange of a set is the arithmetic mean of the greatest and least values, which here are and . This makes the midrange $\frac{A+F}{2}$ .

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Example Question #466 : Arithmetic

A large group of students is given a standardized test. The following information is given about the scores:

Mean: 73.8

Standard deviation: 6.3

Median: 71

25th percentile: 61

75th percentile: 86

Highest score: 100

Lowest score: 12

What is the interquartile range of the tests?

Possible Answers:

More information about the scores is needed.

12.6

2.8

Correct answer:

Explanation:

The interquartile range of a data set is the difference between the 75th and 25th percentiles:

$\textrm{IQR }= 86-61=25$

All other given information is extraneous to the problem.

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Example Question #1 : Arithmetic Mean

Salaries for employees at ABC Company: 1 employee makes $25,000 per year, 4 employees make $40,000 per year, 2 employees make $50,000 per year and 5 employees make $75,000 per year.

What is the average (arithmetic mean) salary for the employees at ABC Company?

Possible Answers:

$\dpi{100} \small \$ 53,500$

$\dpi{100} \small \$ 48,640$

$\dpi{100} \small \$ 46,250$

$\dpi{100} \small \$ 55,000$

$\dpi{100} \small \$ 58,000$

Correct answer:

$\dpi{100} \small \$ 55,000$

Explanation:

The average is found by calculating the total payroll and then dividing by the total number of employees. $\frac{(1\cdot 25,000)+(4\cdot 40,000)+(2\cdot 50,000)+(5\cdot 75,000)}{1+4+2+5}$

$\frac{25,000+160,000+100,000+375,000}{12} = \frac{660,000}{12}= $55,000$

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Example Question #2 : Arithmetic Mean

A bowler had an average (arithmetic mean) score of 215 on the first 5 games she bowled. What must she bowl on the 6th game to average 220 overall?

Possible Answers:

$\dpi{100} \small 145$

$\dpi{100} \small 225$

$\dpi{100} \small 25$

$\dpi{100} \small 258$

$\dpi{100} \small 245$

Correct answer:

$\dpi{100} \small 245$

Explanation:

For the first 5 games the bowler has averaged 215. The equation to calculate the answer is

$\frac{(215\cdot 5)+x}{6}=220$

where $\dpi{100} \small x$ is the score for the sixth game. Next, to solve for the score for the 6th game $\dpi{100} \small (x)$ multiply both sides by 6:

$(215\cdot 5)+x =1,320$

which simplifies to:

$1,075+x =1,320$

After subtracting 1,075 from each side we reach the answer:

$x =1,320 - 1, 075 = 245$

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Example Question #3 : Arithmetic Mean

Ashley averaged a score of 87 on her first 5 tests. She scored a 93 on her 6th test. What is her average test score, assuming all 6 tests are weighted equally?

Possible Answers:

$\dpi{100} \small 92$

$\dpi{100} \small 90$

$\dpi{100} \small 87$

$\dpi{100} \small 91$

$\dpi{100} \small 88$

Correct answer:

$\dpi{100} \small 88$

Explanation:

We can't just average 87 and 93! This will give the wrong answer! The average formula is $\dpi{100} \small average = \frac{sum}{number\ of\ terms}$ .

For the first 5 tests, $\dpi{100} \small 87=\frac{sum}{5}$ . Then $\dpi{100} \small sum=87\times 5=435$ .

Now combine that with the 6th test to find the overall average.

$\dpi{100} \small average = \frac{435+93}{6}=88$

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Example Question #1 : Arithmetic Mean

Sabrina made $3,000 a month for three months, $4,000 the next month, and $5,200 a month for the following two months. What was her average monthly income for the 6 month period?

Possible Answers:

$\dpi{100} \small \$ 4200$

$\dpi{100} \small \$ 4500$

$\dpi{100} \small \$ 4950$

$\dpi{100} \small \$ 3400$

$\dpi{100} \small \$ 3900$

Correct answer:

$\dpi{100} \small \$ 3900$

Explanation:

$\dpi{100} \small average = \frac{3\times 3000 + 4000 + 2\times 5200}{6} = \$ 3900$

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Example Question #2021 : Problem Solving Questions

Luke counts the number of gummy bears he eats every day for 1 week: {39, 18, 24, 51, 40, 15, 23}. On average, how many gummy bears does Luke eat each day?

Possible Answers:

$\dpi{100} \small 27$

$\dpi{100} \small 25$

$\dpi{100} \small 37$

$\dpi{100} \small 30$

$\dpi{100} \small 41$

Correct answer:

$\dpi{100} \small 30$

Explanation:

$average = \frac{39+18+24+51+40+15+23}{7} = 30$

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GMAT Math : Descriptive Statistics

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #463 : Arithmetic

Example Question #11 : Descriptive Statistics

Example Question #465 : Arithmetic

Example Question #14 : Descriptive Statistics

Example Question #466 : Arithmetic

Example Question #1 : Arithmetic Mean

Example Question #2 : Arithmetic Mean

Example Question #3 : Arithmetic Mean

Example Question #1 : Arithmetic Mean

Example Question #2021 : Problem Solving Questions

All GMAT Math Resources

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