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Algebra II : Basic Statistics

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Example Questions

Example Question #211 : Basic Statistics

Determine the mean of the numbers: [-6,8,-31,0,29,0]

Possible Answers:

$\textup{There is no mean.}$

$\frac{37}{3}$

Correct answer:

Explanation:

Add all the numbers in the data set.

(-6)+8+(-31)+0+29+0 = 0

Divide this value by 6, since there are six numbers.

The answer is:

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Example Question #89 : Mean

Determine the mean of the data set: [-9,6,37,0,1,0,4]

Possible Answers:

$\frac{57}{7}$

$\frac{39}{5}$

$\frac{39}{7}$

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

Correct answer:

$\frac{39}{7}$

Explanation:

In order to determine the mean of the set of numbers, sum all the numbers provided.

-9+6+37+1+4 = 39

Since there are seven numbers given, we will need to divide this value by seven.

The answer is: $\frac{39}{7}$

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Example Question #211 : Basic Statistics

Determine the mean of the numbers provided: $[6,-9,\frac{1}{2},-\frac{11}{2}, \frac{4}{3}]$

Possible Answers:

$-\frac{4}{3}$

$-\frac{28}{15}$

$-\frac{100}{3}$

$\frac{13}{15}$

$\frac{28}{15}$

Correct answer:

$-\frac{4}{3}$

Explanation:

Add all the numbers.

$6+(-9)+\frac{1}{2}+(-\frac{11}{2})+ \frac{4}{3} = -3-\frac{10}{2}+\frac{4}{3}$

$=-3-\frac{10}{2}+\frac{4}{3} = -3-5+\frac{4}{3} = -8+\frac{4}{3} = -\frac{24}{3}+\frac{4}{3}$

The sum is $-\frac{20}{3}$ .

Divide this value by five since there are five numbers. This is similar to multiplying by one-fifth.

$-\frac{20}{3} \cdot \frac{1}{5} = -\frac{4}{3}$

The answer is: $-\frac{4}{3}$

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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 #212 : Basic Statistics

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

Possible Answers:

$\frac{18}{7}$

$\frac{12}{7}$

$\textup{There is no mean.}$

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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Algebra II : Basic Statistics

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #211 : Basic Statistics

Example Question #89 : Mean

Example Question #211 : Basic Statistics

Example Question #91 : Mean

Example Question #92 : Mean

Example Question #212 : Basic Statistics

Example Question #94 : Mean

Example Question #93 : Mean

Example Question #212 : Basic Statistics

Example Question #94 : Mean

All Algebra II Resources

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