GMAT Math : Descriptive Statistics

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Example Question #491 : Arithmetic

What is the mean for the following set:

{1,2,8,9,7,4,1,1,3,2,3}

Possible Answers:

3.2

4.5

3.72

Correct answer:

3.72

Explanation:

The mean is the average of all of the numbers:

$\frac{{1+2+8+9+7+4+1+1+3+2+3}}{11}$

$=\frac{{41}}{11}$

=3.72

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Example Question #22 : Calculating Arithmetic Mean

Consider the data set $\left \{ 1, -2, 3, -4, 5, -6, 7, -8, 9, -10 \right \}$

What is its mean?

Possible Answers:

-0.5

0.5

Correct answer:

-0.5

Explanation:

Add the ten elements and divide the sum by 10. The mean is

$\left [ 1+ \left ( -2 \right )+3 +\left ( -4 \right )+5+ \left ( -6 \right )+7+ \left ( -8 \right )+9+\left ( -10 \right ) \right ] \div 10$

$= -5 \div 10 = -0.5$

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Example Question #43 : Descriptive Statistics

A gymnastics meet has seven judges. After each routine, each judge assigns a merit-based score from 0 to 10. To guard against bias, a contestant's score for the routine is the mean of all the judges' scores except for the highest and the lowest.

On one of Sarah's routines, each of the following judges scores her as follows:

$\begin{matrix} \textrm{Davis}& 9.3\\ \textrm{Ellis}& 9.5\\ \textrm{Hanks}& 9.0\\ \textrm{Jones}& 8.4\\ \textrm{Pratt}&9.2 \\ \textrm{Quinn}&9.2 \\ \textrm{Wayne}&8.7 \end{matrix}$

What is Sarah's score?

Possible Answers:

9.28

9.08

9.23

9.13

9.18

Correct answer:

9.08

Explanation:

Ellis and Jones gave Sarah the highest and lowest scores, respectively, so her score will be the mean of the other five:

$\left (9.3+ 9.0+9.2+9.2+8.7 \right )\div 5 =\left (45.4\right )\div 5 = 9.08$

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Example Question #44 : Descriptive Statistics

Find such that the arithmetic mean of n, 13, 27, 35 is equal to the arithmetic mean of 20, 16, 41, 23.

Possible Answers:

Correct answer:

Explanation:

The formula for the arithmetic mean is:

Mean= $\frac{x_{1}+x_{2}+...+x_{n}}{n}$

We can then write:

$\frac{n+13+27+35}{4}=\frac{20+16+41+23}{4}$

n+13+27+35=20+16+41+23

n+75=100

n=25

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Example Question #45 : Descriptive Statistics

The arithmetic mean of the set $\left \{ a, b, c, d \right \}$ is 250.

Which of the following is the arithmetic mean of the set $\left \{ a, b, c, d, e\right \}$ ?

Possible Answers:

$200 + \frac{1}{4}e$

$312\frac{1}{2} + \frac{1}{4}e$

$250 + \frac{1}{4}e$

$250 + \frac{1}{5}e$

$200 + \frac{1}{5}e$

Correct answer:

$200 + \frac{1}{5}e$

Explanation:

$\frac{a+b+c+d}{4} = 250$

a+b+c+d = 1,000

a+b+c+d +e = 1,000 + e

$\frac{a+b+c+d +e }{5}= \frac{1,000 + e}{5} = 200 + \frac{1}{5}e$ ,

which is the correct choice.

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Example Question #46 : Descriptive Statistics

Jane's average score in her biology class is currently . What must be Jane's score on the sixth and last test in order for her final average score to be ?

Possible Answers:

105

103

101

107

Correct answer:

107

Explanation:

We are looking for the grade Jane must get on her 6th test in order to raise her average of 65 from the 5 previous tests to 72.

The sum of Jane's grades from the previous 5 tests is obtained by using the formula of the arithmetic mean.

mean = sum of values/ number of values

sum of values = mean x number of values

$=65\times5=325$

Let x be Jane's score on the 6th test:

$\frac{325+x}{6}=72$

325+x=432

x=432-325

x=107

Jane must get a score of 107 on her last test in order to get an average score of 72 in her class.

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Example Question #41 : Descriptive Statistics

If is a negative number, what is the difference between the mean and the median of the following numbers:

n, n+7, n-8, n-3, n+9

Possible Answers:

Correct answer:

Explanation:

To find the median, write the numbers in ascending orders.

n-8, n-3, n, n+7, n+9

Remember the median is the midpoint value with half of the values below it and the other half of the values above it.

The median is the third number which is n.

The mean is:

$\frac{(n-8)+(n-3)+n+(n+7)+(n+9)}{5}=\frac{5n-11+16}{5}$

$=\frac{5n+5}{5}$

=n+1

mean - median = n+1-n=1

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Example Question #48 : Descriptive Statistics

The arithmetic mean of the set $\left \{ a, b, c, d\right \}$ is 100.

Which of these expressions is equal to the arithmetic mean of the set $\left \{ a, b, c \right \}$ ?

Possible Answers:

$100 - \frac{1}{3}d$

$75 - \frac{1}{3}d$

$133\frac{1}{3} - \frac{1}{3}d$

$100 - \frac{1}{4}d$

$75 - \frac{1}{4}d$

Correct answer:

$133\frac{1}{3} - \frac{1}{3}d$

Explanation:

$\frac{a+b+c+d}{4} = 100$

a+b+c+d = 400

a+b+c = 400 - d

$\frac{a+b+c }{3}= \frac{400 - d}{3} = \frac{400}{3} - \frac{d}{3} = 133\frac{1}{3} - \frac{1}{3}d$

The arithmetic mean of $\left \{ a, b, c \right \}$ is equal to $133\frac{1}{3} - \frac{1}{3}d$

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Example Question #42 : Descriptive Statistics

The arithmetic mean of the set $\left \{ a, b, c, d, e, f, 100\right \}$ is 250 .

Give the arithmetic mean of the set $\left \{ a, b, c, d, e, f\right \}$ .

Possible Answers:

$308\frac{1}{3}$

225

$235 \frac{5}{7}$

$191\frac{2}{3}$

275

Correct answer:

275

Explanation:

We are told that:

$\frac{a+b+c+d+e+f+100 }{7} = 250$

Multiplying each side by :

$\frac{a+b+c+d+e+f+100 }{7} \cdot 7 = 250 \cdot 7$

a+b+c+d+e+f+100 =1,750

Subtracting 100 from each side:

a+b+c+d+e+f =1,650

At this point, we can solve for the arithmetic mean of the set $\left \{ a, b, c, d, e, f\right \}$ :

$\frac{a+b+c+d+e+f }{6}=\frac{1,650}{6} = 275$ , the arithmetic mean of the set $\left \{ a, b, c, d, e, f\right \}$ .

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Example Question #50 : Descriptive Statistics

A bakery sold a daily average of 25 croissants last week. The table above shows the number of croissants sold each day except Sunday. Find the number of croissants sold on Sunday.

Possible Answers:

Correct answer:

Explanation:

Let be the number of croissants sold on Sunday. The daily average of croissants sold in the past week is:

$\frac{29+15+12+10+34+38+x}{7}=25$

Solve for :

29+15+12+10+34+38+x=175

138+x=175

x=175-138=37

The number of croissants sold on Sunday is .

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GMAT Math : Descriptive Statistics

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #491 : Arithmetic

Example Question #22 : Calculating Arithmetic Mean

Example Question #43 : Descriptive Statistics

Example Question #44 : Descriptive Statistics

Example Question #45 : Descriptive Statistics

Example Question #46 : Descriptive Statistics

Example Question #41 : Descriptive Statistics

Example Question #48 : Descriptive Statistics

Example Question #42 : Descriptive Statistics

Example Question #50 : Descriptive Statistics

All GMAT Math Resources

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