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Algebra II : Mean

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Example Question #51 : Mean

Find the mean given the data set: [12,-3,6,-8,1]

Possible Answers:

$\frac{14}{5}$

$\textup{The mean does not exist.}$

$\frac{24}{5}$

$\frac{8}{5}$

Correct answer:

$\frac{8}{5}$

Explanation:

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

Add all the numbers and divide them by the total amount of numbers given.

12+(-3)+6+(-8)+1 = 8

There are five numbers.

Divide the sum by five.

The mean is: $\frac{8}{5}$

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Example Question #52 : Mean

Find the mean of the data set: [1,0.1,0.01,3]

Possible Answers:

1.275

1.0275

0.55

1.025

Correct answer:

1.0275

Explanation:

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

Sum all the numbers.

1+0.1+0.01+3 =4.11

Divide this number by four.

$\frac{4.11}{4}=1.0275$

The mean is: 1.0275

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Example Question #53 : Mean

Determine the mean of the data set: $[\frac{2}{5}, \frac{1}{3}, \frac{7}{4},-2]$

Possible Answers:

$\frac{37}{120}$

$\frac{59}{240}$

$\frac{269}{240}$

$\frac{29}{240}$

$\frac{47}{120}$

Correct answer:

$\frac{29}{240}$

Explanation:

The mean is the sum of the numbers in the data set.

Add all the numbers. To add the fractions, we will need to find the least common denominator.

Multiply all the denominators together.

$5\times 3\times 4 = 60$

Convert all the numbers with a denominator of 60. What is multiplied on the bottom must be multiplied on the top as well.

$\frac{2}{5}+\frac{1}{3}+ \frac{7}{4}+(-2) = \frac{2(4)(3)}{5(4)(3)}+\frac{1(4)(5)}{3(4)(5)}+\frac{7(3)(5)}{4(3)(5)}-\frac{2(4)(3)(5)}{1(4)(3)(5)}$

Simplify all the fractions.

$\frac{24}{60}+\frac{20}{60}+\frac{105}{60}-\frac{120}{60} = \frac{29}{60}$

Divide this fraction by four to find the mean. Dividing by four is the same as multiplying by one-fourth.

$\frac{29}{60}\times \frac{1}{4} = \frac{29}{240}$

The answer is: $\frac{29}{240}$

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Example Question #54 : Mean

Determine the mean of the data set: [-5,6,-9,18]

Possible Answers:

$\textup{There is no mean.}$

$\frac{5}{2}$

$-\frac{13}{2}$

$\frac{13}{2}$

$-\frac{1}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

The mean of a data set is the average of all the numbers provided.

Sum all the numbers.

-5+6-9+18 = 10

Divide this number by the total numbers in the data set.

$\frac{10}{4}= \frac{5}{2}$

The answer is: $\frac{5}{2}$

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Example Question #55 : Mean

Solve for the mean: [9,10,23,56,107,108]

Possible Answers:

$\frac{323}{6}$

$\frac{79}{2}$

$\frac{313}{6}$

$\frac{101}{2}$

$\textup{There is no mean.}$

Correct answer:

$\frac{313}{6}$

Explanation:

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

There are six numbers provided.

Sum all the numbers and divide by six.

$\frac{9+10+23+56+107+108}{6} = \frac{313}{6}$

The answer is: $\frac{313}{6}$

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Example Question #56 : Mean

Find the mean of the data set: [9,3,4,7,6,4]

Possible Answers:

$\frac{41}{3}$

$\frac{11}{2}$

$\frac{11}{6}$

$\frac{33}{5}$

Correct answer:

$\frac{11}{2}$

Explanation:

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

Add the numbers.

9+3+4+7+6+4= 33

Divide this number by six, since there are six numbers given in the problem.

$\frac{33}{6} = \frac{3\times 11}{3\times 2}$

Reduce this fraction.

The answer is: $\frac{11}{2}$

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Example Question #51 : Mean

Find the mean of the following data set. [-1,-5,-8,17,41]

Possible Answers:

$\frac{44}{5}$

$\frac{22}{5}$

$\frac{49}{5}$

$-\frac{49}{5}$

Correct answer:

$\frac{44}{5}$

Explanation:

To determine the mean, sum all the numbers and divide the sum by the total numbers in the data set.

-1+(-5)+(-8)+17+41=44

Divide this number by five.

The mean is: $\frac{44}{5}$

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Example Question #58 : Mean

If Richard scored an 80, 20, 30, and 50 on four of his five exams, what score must he make on his last exam to pass the class, assuming that the passing score is 80 out of 100 possible points?

Possible Answers:

100

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

Correct answer:

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

Explanation:

In order to solve for Richard's final grade, we will need to set up an equation such that the average of all five scores will equal to eighty.

Let the unknown test score represent .

$\frac{80+20+30+50+x}{5} = 80$

Multiply by five on both sides to eliminate the denominator.

$\frac{80+20+30+50+x}{5} \times 5= 80 \times 5$

Simplify both sides.

180+x=400

Subtract 180 from both sides of the equation.

180+x-180=400-180

x=220

Since this score is beyond the highest possible score that Richard earn on his last exam, he cannot pass no matter what his grade is.

The answer is: $\textup{Richard cannot pass the class.}$

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Example Question #59 : Mean

Suppose Billy has two dollars. Susie has a fourth of what Billy has. Katie has about a third of what Susie has. What is the approximate mean of the three amounts?

Possible Answers:

$\$0.83$

$\$0.89$

$\$0.78$

$\$0.68$

$\$0.98$

Correct answer:

$\$0.89$

Explanation:

Set up variables using the first letter of each person's name to identify the actual amount of money for the three individuals.

$B=\$2$

$S=\frac{1}{4}B=\frac{1}{4}(\$2) = \$0.50$

$K=\frac{1}{3}S = \frac{1}{3}(\$0.50) = \$0.1\bar{6}=\$0.17$

Katie's amount is rounded to the nearest cent.

Add the three values and divide the quantity by three to obtain the mean.

$\$2+\$0.50+\$0.17 = \$2.67$

Divide this total by three.

$\frac{ \$2.67}{3} = \$0.89$

The mean is: $\$0.89$

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Example Question #151 : Data Properties

Determine the mean of the set of numbers: [-1,-2,3,4,-5,30]

Possible Answers:

$\frac{29}{6}$

$\frac{25}{6}$

$\frac{11}{3}$

$\frac{27}{6}$

$\frac{13}{3}$

Correct answer:

$\frac{29}{6}$

Explanation:

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

Add all the numbers.

-1+(-2)+3+4+(-5)+30=29

Since there are six numbers, divide this sum by six.

The answer is: $\frac{29}{6}$

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Algebra II : Mean

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #51 : Mean

Example Question #52 : Mean

Example Question #53 : Mean

Example Question #54 : Mean

Example Question #55 : Mean

Example Question #56 : Mean

Example Question #51 : Mean

Example Question #58 : Mean

Example Question #59 : Mean

Example Question #151 : Data Properties

All Algebra II Resources

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