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Algebra II : Data Properties

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Example Questions

Example Question #191 : Data Properties

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

Possible Answers:

$\frac{18}{7}$

$\textup{There is no mean.}$

$\frac{12}{7}$

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 #192 : Data Properties

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 #193 : Data Properties

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

Possible Answers:

$\frac{19}{2}$

$\frac{121}{5}$

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 #193 : Data Properties

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:

100

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

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 #194 : Data Properties

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

Possible Answers:

4.1

5.1

4.01

3.5

4.05

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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Example Question #195 : Data Properties

Determine the mean: [-9,18,33,10,3]

Possible Answers:

Correct answer:

Explanation:

Add all the numbers in the data set.

-9+18+33+10+3 = 55

Divide this value by five.

$\frac{55}{5}=11$

The answer is:

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Example Question #102 : Mean

Determine the mean of the values: [-56,71,88,97]

Possible Answers:

$\textup{There is no mean.}$

$\frac{159}{2}$

151

Correct answer:

Explanation:

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

Add the numbers together.

-56+71+88+97 = 200

Divide this value by four to get the mean.

$\frac{200}{4} = 50$

The answer is:

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Example Question #102 : Mean

Determine the exact mean of the numbers: $[\frac{1}{2}, \sqrt{9}, \sqrt{8}]$

Possible Answers:

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

$\frac{2}{9}+\frac{4\sqrt2}{3}$

$\frac{2}{9}+\frac{2\sqrt2}{3}$

$\frac{2}{9}+\frac{4\sqrt2}{9}$

$\frac{7}{6}+\frac{2\sqrt2}{3}$

Correct answer:

$\frac{7}{6}+\frac{2\sqrt2}{3}$

Explanation:

The mean is the sum of all terms in the data set, divided by the total amount of numbers given.

$\sqqrt8 = \sqrt4 \cdot \sqrt2 =2\sqrt2$

$\frac{\frac{1}{2}+\sqrt9 +\sqrt{8}}{3} = \frac{\frac{1}{2}+3 +2\sqrt{2}}{3} = \frac{\frac{1}{2}+\frac{6}{2} +2\sqrt{2}}{3}$

Combine like terms.

$\frac{\frac{7}{2} +2\sqrt{2}}{3}$

Dividing by three is similar to multiplying by one-third.

$\frac{\frac{7}{2} +2\sqrt{2}}{3}=\frac{1}{3}(\frac{7}{2} +2\sqrt{2})$

The answer is: $\frac{7}{6}+\frac{2\sqrt2}{3}$

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Example Question #104 : Mean

Determine the mean of the numbers: [0.3,3.33,2.5,0.5,1.69]

Possible Answers:

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

1.664

1.690

1.683

1.670

Correct answer:

1.664

Explanation:

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

Sum the numbers and divide by the total amount of numbers.

$\frac{0.3+3.33+2.5+0.5+1.69}{5}= \frac{8.32}{5}$

Divide the two numbers.

The answer is: 1.664

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Example Question #105 : Mean

Determine the mean of the following numbers: [-9,-18,31,4,7]

Possible Answers:

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

Correct answer:

Explanation:

The mean is the average of all the numbers.

Add all the numbers in the data set.

(-9)+(-18)+31+4+7 =15

Divide this number by five.

$\frac{15}{5 }=3$

The answer is:

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Algebra II : Data Properties

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #191 : Data Properties

Example Question #192 : Data Properties

Example Question #193 : Data Properties

Example Question #193 : Data Properties

Example Question #194 : Data Properties

Example Question #195 : Data Properties

Example Question #102 : Mean

Example Question #102 : Mean

Example Question #104 : Mean

Example Question #105 : Mean

All Algebra II Resources

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