Arithmetic Mean - GMAT Quantitative

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Question

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 $\left \{ a, b, c, d, e\right \}$ ?

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Answer

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

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

which is the correct choice.

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Question

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

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Answer

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes

$\frac{A +B+ C+D+E }{5}$

the correct choice.

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Question

What is the mean of this data set?

$\left \{ 1, 0.1, 0.01, 0.001, 0.0001, 0.00001 \right \}$

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Answer

Add the numbers and divide by 6:

$\left (1 + 0.1 + 0.01 + 0.001+ 0.0001 + 0.00001 \right )\div 6$

$= 1.11111\div 6 = 0.185185$

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Question

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?

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Answer

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 .

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Question

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 ?

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Answer

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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Question

What is the mean of this data set?

$\left \{ 1, 0.1, 0.01, 0.001, 0.0001, 0.00001 \right \}$

Tap to reveal answer

Answer

Add the numbers and divide by 6:

$\left (1 + 0.1 + 0.01 + 0.001+ 0.0001 + 0.00001 \right )\div 6$

$= 1.11111\div 6 = 0.185185$

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Question

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?

Tap to reveal answer

Answer

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 .

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Question

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 ?

Tap to reveal answer

Answer

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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Question

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?

Tap to reveal answer

Answer

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 .

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Question

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 ?

Tap to reveal answer

Answer

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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Question

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 $\left \{ a, b, c, d, e\right \}$ ?

Tap to reveal answer

Answer

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

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

which is the correct choice.

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Question

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 $\left \{ a, b, c, d, e\right \}$ ?

Tap to reveal answer

Answer

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

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

which is the correct choice.

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Question

What is the mean of the following data set in terms of and ?

$\left \{a -x, a, a + x, a + 2x, 2a-x, 2a, 2a+x, 2a+2x \right \}$

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Answer

Add the expressions and divide by the number of terms, 8.

The sum of the expressions is:

$\left (a -x \right ) + a + \left ( a + x \right ) +\left ( a +2x \right ) + \left ( 2a-x \right ) + 2a + \left ( 2a+x \right ) +\left ( 2a+2x \right )$

Divide this by 8:

$\left ( 12a + 4x \right )\div 8 =\frac{3}{2} a +\frac{1}{2} x$

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Question

What is the mean of this data set?

$\left \{ 1, 0.1, 0.01, 0.001, 0.0001, 0.00001 \right \}$

Tap to reveal answer

Answer

Add the numbers and divide by 6:

$\left (1 + 0.1 + 0.01 + 0.001+ 0.0001 + 0.00001 \right )\div 6$

$= 1.11111\div 6 = 0.185185$

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Question

What is the mean of the following data set in terms of and ?

$\left \{a -x, a, a + x, a + 2x, 2a-x, 2a, 2a+x, 2a+2x \right \}$

Tap to reveal answer

Answer

Add the expressions and divide by the number of terms, 8.

The sum of the expressions is:

$\left (a -x \right ) + a + \left ( a + x \right ) +\left ( a +2x \right ) + \left ( 2a-x \right ) + 2a + \left ( 2a+x \right ) +\left ( 2a+2x \right )$

Divide this by 8:

$\left ( 12a + 4x \right )\div 8 =\frac{3}{2} a +\frac{1}{2} x$

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Question

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

What is its mean?

Tap to reveal answer

Answer

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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Question

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 $\left \{ a, b, c, d, e\right \}$ ?

Tap to reveal answer

Answer

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

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

which is the correct choice.

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Question

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

Tap to reveal answer

Answer

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes

$\frac{A +B+ C+D+E }{5}$

the correct choice.

← Didn't Know|Knew It →

Question

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 $\left \{ a, b, c, d, e\right \}$ ?

Tap to reveal answer

Answer

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

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

which is the correct choice.

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

Answer

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes

$\frac{A +B+ C+D+E }{5}$

the correct choice.

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Knew It

Arithmetic Mean - GMAT Quantitative

The arithmetic mean of the set is 250. Which of the following is the arithmetic mean of the set ?

, which is the correct choice.

Give the arithmetic mean of the set .

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes the correct choice.

What is the mean of this data set?

Add the numbers and divide by 6:

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

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

Divide the sum of the eight elements by 8 to get the mean, which must be greater than or equal to 50: This is all that is needed for the set to have mean 50.

What is the mean of this data set?

Add the numbers and divide by 6:

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

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

Divide the sum of the eight elements by 8 to get the mean, which must be greater than or equal to 50: This is all that is needed for the set to have mean 50.

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

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

Divide the sum of the eight elements by 8 to get the mean, which must be greater than or equal to 50: This is all that is needed for the set to have mean 50.

The arithmetic mean of the set is 250. Which of the following is the arithmetic mean of the set ?

, which is the correct choice.

The arithmetic mean of the set is 250. Which of the following is the arithmetic mean of the set ?

, which is the correct choice.

What is the mean of the following data set in terms of and ?

Add the expressions and divide by the number of terms, 8. The sum of the expressions is: Divide this by 8:

What is the mean of this data set?

Add the numbers and divide by 6:

What is the mean of the following data set in terms of and ?

Add the expressions and divide by the number of terms, 8. The sum of the expressions is: Divide this by 8:

Consider the data set What is its mean?

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

The arithmetic mean of the set is 250. Which of the following is the arithmetic mean of the set ?

, which is the correct choice.

Give the arithmetic mean of the set .

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes the correct choice.

The arithmetic mean of the set is 250. Which of the following is the arithmetic mean of the set ?

, which is the correct choice.

Give the arithmetic mean of the set .

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes the correct choice.

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 $\left \{ a, b, c, d, e\right \}$ ?

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

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

which is the correct choice.

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

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes

$\frac{A +B+ C+D+E }{5}$

the correct choice.

What is the mean of this data set?

$\left \{ 1, 0.1, 0.01, 0.001, 0.0001, 0.00001 \right \}$

Add the numbers and divide by 6:

$\left (1 + 0.1 + 0.01 + 0.001+ 0.0001 + 0.00001 \right )\div 6$

$= 1.11111\div 6 = 0.185185$

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?

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 ?

What is the mean of this data set?

$\left \{ 1, 0.1, 0.01, 0.001, 0.0001, 0.00001 \right \}$

Add the numbers and divide by 6:

$\left (1 + 0.1 + 0.01 + 0.001+ 0.0001 + 0.00001 \right )\div 6$

$= 1.11111\div 6 = 0.185185$

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?

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 ?

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?

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 ?

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 $\left \{ a, b, c, d, e\right \}$ ?

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

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

which is the correct choice.

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 $\left \{ a, b, c, d, e\right \}$ ?

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

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

which is the correct choice.

What is the mean of the following data set in terms of and ?

$\left \{a -x, a, a + x, a + 2x, 2a-x, 2a, 2a+x, 2a+2x \right \}$

What is the mean of this data set?

$\left \{ 1, 0.1, 0.01, 0.001, 0.0001, 0.00001 \right \}$

Add the numbers and divide by 6:

$\left (1 + 0.1 + 0.01 + 0.001+ 0.0001 + 0.00001 \right )\div 6$

$= 1.11111\div 6 = 0.185185$

What is the mean of the following data set in terms of and ?

$\left \{a -x, a, a + x, a + 2x, 2a-x, 2a, 2a+x, 2a+2x \right \}$

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

What is its mean?

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

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

$= -5 \div 10 = -0.5$

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 $\left \{ a, b, c, d, e\right \}$ ?

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

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

which is the correct choice.

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

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes

$\frac{A +B+ C+D+E }{5}$

the correct choice.

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 $\left \{ a, b, c, d, e\right \}$ ?

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

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

which is the correct choice.

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

The arithmetic mean of a set is the sum of its elements divided by the number of elements, which here is . This makes

$\frac{A +B+ C+D+E }{5}$

the correct choice.