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Algebra II : Data Properties

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Example Questions

Example Question #243 : Algebra Ii

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

Possible Answers:

$\frac{11}{6}$

$\frac{41}{3}$

$\frac{11}{2}$

$\frac{33}{5}$

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:

$\frac{49}{5}$

$-\frac{49}{5}$

$\frac{44}{5}$

$\frac{22}{5}$

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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Example Question #61 : Mean

Solve for the mean: [0,0,10,-20,30,1,4,9]

Possible Answers:

$\frac{17}{8}$

$\frac{11}{2}$

$\frac{17}{2}$

$\frac{17}{4}$

$\frac{17}{3}$

Correct answer:

$\frac{17}{4}$

Explanation:

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

Add all the numbers.

0+0+10+(-20)+30+1+4+9 =34

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

$\frac{34}{8}$

Reduce this fraction.

The answer is: $\frac{17}{4}$

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Example Question #61 : Mean

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

Possible Answers:

$\frac{49}{12}$

$\frac{55}{4}$

$\frac{55}{12}$

$\frac{55}{48}$

$\frac{49}{48}$

Correct answer:

$\frac{49}{48}$

Explanation:

Add all the numbers in the data set.

$1+\frac{1}{3}+ (-\frac{1}{4})+ 3$

Convert all numbers and fractions to a least common denominator.

The least common denominator is 12 because this is the least number divisible by every denominator.

$1+\frac{1}{3}-\frac{1}{4}+ 3 =\frac{12}{12} +\frac{4}{12}-\frac{3}{12}+\frac{36}{12}$

Since all the denominators are common, we can add and subtract the numerators.

$\frac{49}{12}$

Divide this number by four, or multiply by one-fourth, since there are four numbers in the data set.

$\frac{49}{12}\times \frac{1}{4} =\frac{49}{48}$

The mean is: $\frac{49}{48}$

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Example Question #62 : Mean

Sarah is to compete in 4 areas at a gymnastics competition . On high bar, floor, and on vault, she scored a 9.4, 8.9, and a 9.8. The maximum score is 10. If placing top three in the competition requires her to score at least a 9.5 overall, what must she score on balance beam?

Possible Answers:

9.85

9.8

$\textup{Sarah will need to score higher than 10 to earn awards.}$

9.9

9.95

Correct answer:

9.9

Explanation:

The average is already known. What is not known is Sarah's balance beam score.

Set up an equation such that the quantity of the four scores including the unknown score divided by four is equal to 9.5. Let the score of the balance beam routine be .

$\frac{9.4+8.9+9.8+x}{4}=9.5$

Multiply both sides by four to eliminate the denominator and simplify the numerator.

$(\frac{9.4+8.9+9.8+x}{4})\times 4=9.5\times 4$

28.1+x=38

Subtract 28.1 from both sides to determine the unknown variable.

x=9.9

Sarah's score must be a 9.9 or higher to earn awards.

The answer is: 9.9

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Example Question #63 : Mean

Bob scores a 5, 6, and 7 on three of four tests. The highest possible score is a ten. What must he score on his next test to average an overall score of 8?

Possible Answers:

9.9

9.5

$\textup{Bob cannot average an overall score of 8.}$

Correct answer:

$\textup{Bob cannot average an overall score of 8.}$

Explanation:

Set up an equation such that the average of Bob's three grades and his unknown fourth test grade is equal to eight.

$\frac{5+6+7+x}{4}= 8$

Multiply both sides of the equation by four.

$\frac{5+6+7+x}{4}\times 4= 8\times 4$

Simplify both sides.

5+6+7+x = 32

18+x=32

Subtract 18 from both sides.

18+x-18=32-18

x=14

Bob is unable to average an 8 overall score since he would have to make a 14 on his final test grade, which is impossible since 10 is the highest score he can earn.

The answer is: $\textup{Bob cannot average an 8 overall score.}$

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Example Question #251 : Algebra Ii

Determine the mean of the numbers: [2,9,32,88,10,-5,7]

Possible Answers:

$\frac{143}{7}$

$\frac{148}{7}$

Correct answer:

$\frac{143}{7}$

Explanation:

In order to determine the mean of the set of numbers, sum the numbers provided and divide the sum by the total amount of numbers.

2+9+32+88+10+(-5)+7=143

Divide this number by seven.

The mean is: $\frac{143}{7}$

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Algebra II : Data Properties

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #243 : Algebra Ii

Example Question #51 : Mean

Example Question #58 : Mean

Example Question #59 : Mean

Example Question #151 : Data Properties

Example Question #61 : Mean

Example Question #61 : Mean

Example Question #62 : Mean

Example Question #63 : Mean

Example Question #251 : Algebra Ii

All Algebra II Resources

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