GMAT Math : Calculating arithmetic mean

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Example Question #21 : Calculating Arithmetic Mean

Consider the data set $\left \{ 1, 3, 4, 6, 6, 7, 7, 7, 9, 10\right \}$ .

Which of the following is true about the median and the mean of the data set?

Possible Answers:

The median exceeds the mean by 0.5.

The median exceeds the mean by 1.

The mean and the median are equal.

The mean exceeds the median by 1.

The mean exceeds the median by 0.5.

Correct answer:

The median exceeds the mean by 0.5.

Explanation:

The mean of the data set is the sum of the elements divided by the size of the set, which is ten:

$\frac{1+3+ 4+ 6+ 6+ 7+ 7+ 7+ 9+ 10}{10} = \frac{60}{10} = 6$

The median of a data set with an even number of elements is the arithmetic mean of the two elements that fall in the middle when the elements are arranged in ascending order. These two elements are 6 and 7, so the median is $\frac{6+7}{2} = 6.5$ .

The median is greater than the mean by 6.5-6 = 0.5 .

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Example Question #21 : Arithmetic Mean

The mean of the following terms is 11. Solve for .

15, 12, 9, 7, 17, 8,

Possible Answers:

x=10

x=11

x=8

x=9

Correct answer:

x=9

Explanation:

The mean times the number of terms is equal to 77.

$7\times11=77$

The sum of all of the terms must equal 77.

15+12+9+7+17+8+x=77

68+x=77

x=9

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Example Question #32 : Descriptive Statistics

Charlotte's course average in chemistry class is the average of the best five of her six hourly test scores. Going into finals week, Charlotte has scores of 88, 84, 84, 89, and 72. How much, at minimum, must Charlotte score on her sixth test in order to make an average of 85 or better for the term?

Possible Answers:

Charlotte is already assured of a course average of at least 85 for the term.

Correct answer:

Explanation:

If Charlotte does not take the sixth test, she will receive the average of her first five tests - this is

$\frac{88 + 84+ 84+ 89+ 72}{5} = \frac{417}{5} = 83.4$

Charlotte is not assured of an 85 or better, so she must take the test to achieve this.

Let be the score she makes on the sixth test. If $x \leq 72$ , then her first five tests will stand, so let's assume that x > 72 . Then her average will be

$\frac{88 + 84+ 84+ 89+ x}{5} =\frac{x + 345}{5}$

Since Charlotte wants an average of 85 or better, we solve this inequality:

$\frac{x + 345}{5} \geq 85$

$\frac{x + 345}{5}\cdot 5\geq 85\cdot 5$

$x + 345\geq 425$

$x + 345-345 \geq 425-345$

$x \geq 80$

Her sixth test must be 80, at minimum.

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Example Question #33 : Descriptive Statistics

Consider the data set

$\left \{ 65, 32, 89, 44, 90, 33, M, N\right \}$

For the set to have mean greater than or equal to 50, what must hold true about and ?

Possible Answers:

One must be greater than 94; the other must be less than 94.

Their sum must be greater than or equal to 47.

Each must be greater than or equal to 47.

Their sum must be greater than or equal to 94.

One must be greater than 47; the other must be less than 47.

Correct answer:

Their sum must be greater than or equal to 47.

Explanation:

Divide the sum of the eight elements by 8 to get the mean, which must be greater than or equal to 50:

$\frac{65+32+89+44+90+33+M+N }{8} \geq 50$

$\frac{353+M+N }{8} \geq 50$

$\frac{353+M+N }{8} \cdot 8\geq 50 \cdot 8$

$353+M+N \geq 400$

$353+M+N -353 \geq 400-353$

$M+N \geq 47$

This is all that is needed for the set to have mean 50.

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Example Question #31 : Descriptive Statistics

What is the mean for the following data set:

{63,49,68,59,29,62,46,5}

Possible Answers:

47.63

38.10

54.42

40.25

Correct answer:

47.63

Explanation:

The mean is the average of the data set. There are data points in the set

{63,49,68,59,29,62,46,5}

$\frac{{63+49+68+59+29+62+46+5}}{8}$

$\frac{381}{8}$

47.63

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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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GMAT Math : Calculating arithmetic mean

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : Calculating Arithmetic Mean

Example Question #21 : Arithmetic Mean

Example Question #32 : Descriptive Statistics

Example Question #33 : Descriptive Statistics

Example Question #31 : Descriptive Statistics

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

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