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Algebra II : Mean

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Example Question #91 : Mean

Determine the mean of the following numbers: [8,11,9,12,59,132]

Possible Answers:

$\frac{231}{6}$

$\frac{77}{2}$

Correct answer:

$\frac{77}{2}$

Explanation:

The mean is defined as the average of all the numbers given in the data set.

Sum all the numbers, and divide the sum by the total amount of numbers given.

8+11+9+12+59+132 =231

Divide this value by 6.

$\frac{231}{6}$

This fraction is reducible.

$\frac{231}{6} = \frac{77\times 3}{2\times 3} = \frac{77}{2}$

The answer is: $\frac{77}{2}$

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Example Question #92 : Mean

Sally made a 40, 50, and 60 on her first three tests. There are 3 more tests remaining, and the highest score is a 100 points possible on the tests. What must she average on her next three tests in order to pass the class with an overall score of 70?

Possible Answers:

100

$\textup{Sally cannot pass the class.}$

Correct answer:

Explanation:

Set up an equation such that the three known grades and the three unknown grades will average a 70 in the class. Let different variables represent the three unknown tests.

$\frac{40+50+60+x+y+z}{6} = 70$

Multiply by six on both sides.

$\frac{40+50+60+x+y+z}{6} \cdot 6 = 70 \cdot 6$

40+50+60+x+y+z = 420

Simplify the left side.

150+x+y+z = 420

Subtract by 150 on both sides.

150+x+y+z -150= 420-150

x+y+z = 270

The sum of Sally's next three tests must average a 270. This means we need to divide both sides by three to get the average of her three scores.

$\frac{x+y+z}{3} = \frac{270}{3}$

The answer is:

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Example Question #212 : Basic Statistics

Determine the mean of the numbers: [2,90,102,7,4]

Possible Answers:

$\textup{The mean is not given.}$

Correct answer:

Explanation:

The mean is defined as the average of all the numbers provided in the set.

Add the the values in the data set.

2+90+102+7+4 = 205

Divide this value by five, since there are five numbers given.

$\frac{205}{5}=41$

The answer is:

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Example Question #94 : Mean

Richard took five tests in his class. Determine the mean of Richard's test scores:

[90,85,70,50,30]

Possible Answers:

Correct answer:

Explanation:

To determine the mean of the student's test scores, add all the numbers provided in the data set and divide the total by five.

90+85+70+50+30=325

Divide this number by five.

$\frac{325}{5} = 65$

The answer is:

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Example Question #93 : Mean

Determine the mean of the given numbers: [6,9,14,87,4]

Possible Answers:

Correct answer:

Explanation:

The mean is the average of all the given numbers in the data set.

Add all the numbers and divide by five.

6+9+14+87+4 = 120

$\frac{120}{5}=24$

The answer is:

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Example Question #91 : Mean

Determine the mean: [1,-9,3,0,8,4,5]

Possible Answers:

$\frac{12}{7}$

$\frac{18}{7}$

$\textup{There is no mean.}$

Correct answer:

$\frac{12}{7}$

Explanation:

The mean is the average of all the numbers in the data set.

Add the numbers and divide the quantity by seven.

$\frac{1+(-9)+3+0+8+4+5}{7} = \frac{12}{7}$

The answer is: $\frac{12}{7}$

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Example Question #94 : Mean

Determine the mean of the numbers: [7,6,41,87,19]

Possible Answers:

$\textup{The mean cannot be determined.}$

Correct answer:

Explanation:

Add all the numbers.

7+6+41+87+19 = 160

The mean is the average of all the numbers, which means dividing this number by five will give the average.

$\frac{160}{5} =32$

The answer is:

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Example Question #92 : Mean

Determine the mean: [9,19,22,63,-8]

Possible Answers:

$\frac{121}{5}$

$\frac{19}{2}$

Correct answer:

Explanation:

The mean is the average of all the numbers given in the set of data.

Add all the numbers and divide by five, since there are five numbers provided.

$\frac{9+19+22+63+(-8)}{5} = \frac{105}{5}$

The answer is:

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Example Question #99 : Mean

Sam scored a $70,80, \textup{and } 90$ on three of his four tests. If he has one more test, and each of his tests has a maximum of 100 points, what grade must he make on his last test in order to average a in the class?

Possible Answers:

$\textup{The answer is not given.}$

100

Correct answer:

$\textup{The answer is not given.}$

Explanation:

Set up an equation such that the average of Sam's four tests will equal to 90.

$\frac{70+80+90+x}{4}=90$

Solve for x. Multiply by four on both sides.

$\frac{70+80+90+x}{4}\cdot 4=90\cdot 4$

70+80+90+x=360

Add the values on the left.

240+x=360

Subtract 240 from both sides.

240+x-240=360-240

x=120

Since the maximum of each test is 100, Sam cannot achieve a 90 in the class.

The answer is: $\textup{The answer is not given.}$

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Example Question #96 : Mean

Determine the mean of the numbers: [1.2,3.5,9.8,4.7,1.3]

Possible Answers:

4.01

5.1

4.05

3.5

4.1

Correct answer:

4.1

Explanation:

The mean is the average of all the numbers given in the data set.

Add the numbers.

1.2+3.5+9.8+4.7+1.3 = 20.5

Divide this number by five.

$\frac{20.5}{5} = 4.1$

The answer is: 4.1

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Algebra II : Mean

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #91 : Mean

Example Question #92 : Mean

Example Question #212 : Basic Statistics

Example Question #94 : Mean

Example Question #93 : Mean

Example Question #91 : Mean

Example Question #94 : Mean

Example Question #92 : Mean

Example Question #99 : Mean

Example Question #96 : Mean

All Algebra II Resources

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