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Algebra II : Mean

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Example Question #71 : Mean

Determine the mean of the numbers: [-3,-18,-3,99]

Possible Answers:

$\frac{75}{4}$

$\frac{123}{4}$

$\textup{There is no mean.}$

Correct answer:

$\frac{75}{4}$

Explanation:

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

Add all the numbers provided and divide the sum by a total of four, since there are four numbers given.

$\frac{(-3)+(-18)+(-3)+99}{4} = \frac{75}{4}$

This fraction is irreducible.

The answer is: $\frac{75}{4}$

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Example Question #71 : Mean

Determine the mean: [ -9,2,9,20,37]

Possible Answers:

$\frac{59}{5}$

$\frac{77}{5}$

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

Correct answer:

$\frac{59}{5}$

Explanation:

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

Add all the numbers.

-9+2+9+20+37 = 59

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

The answer is: $\frac{59}{5}$

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Example Question #73 : Mean

Determine the mean of the numbers: $[\frac{1}{3},3\%, \frac{1}{30}]$

Possible Answers:

$\frac{119}{900}$

$\frac{119}{300}$

$\frac{19}{90}$

$\frac{19}{30}$

$\frac{1}{30}$

Correct answer:

$\frac{119}{900}$

Explanation:

The mean is the average of all the numbers. Convert the percentage to a fraction by removing the percentage and divide the number by 100.

$[\frac{1}{3},3\%, \frac{1}{30}]\rightarrow[\frac{1}{3}, \frac{3}{100},\frac{1}{30}]$

Convert all fractions to a common denominator. Write out the factors for the denominators.

3-[3,6,9,...,294,297,300]

30-[30,60,90,120,150,180,210,240,270,300]

100-[100,200,300]

The common denominator is 300.

$\frac{1}{3}+ \frac{3}{100}+\frac{1}{30}= \frac{1(100)}{3(100)}+ \frac{3(3)}{100(3)}+\frac{1(10)}{30(10)}$

Simplify the fractions.

$\frac{100}{300}+\frac{9}{300}+\frac{10}{300} = \frac{119}{300}$

There are three numbers in the data set. Divide the fraction by three.

$\frac{ \frac{119}{300}}{3}= \frac{119}{300} \div 3 = \frac{119}{300}\times \frac{1}{3} = \frac{119}{900}$

The answer is: $\frac{119}{900}$

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Example Question #72 : Mean

Determine the mean of the following numbers: [2,8,16,32,56]

Possible Answers:

$\frac{104}{5}$

$\frac{114}{5}$

Correct answer:

$\frac{114}{5}$

Explanation:

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

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

$\frac{2+8+16+32+56}{5}= \frac{114}{5}$

The answer is: $\frac{114}{5}$

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Example Question #75 : Mean

Determine the mean of the numbers: [2,9,1,-3,14,26]

Possible Answers:

$\frac{17}{3}$

$\frac{46}{5}$

$\frac{49}{6}$

$\frac{49}{5}$

$\frac{11}{2}$

Correct answer:

$\frac{49}{6}$

Explanation:

The mean is the sum of all the numbers in the data set over the total amount of numbers given.

Add the numbers.

2+9+1+(-3)+14+26 = 49

Divide this number by six since there are 6 numbers.

The answer is: $\frac{49}{6}$

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Example Question #73 : Mean

The top student of the class makes 95 and 97 on his first two tests. However, he was under pressure and scored a 25 on his third test. There are 2 more tests remaining, and the highest possible score he can make on each test is 100. Can he maintain at least a 90 in his class? If so, what is the mandatory average of his fourth and fifth tests?

Possible Answers:

$\textup{Yes, 95}$

$\textup{Yes, 100}$

$\textup{Yes, 98.5}$

$\textup{Yes, 99.5}$

$\textup{No, it is not possible to maintain the score.}$

Correct answer:

$\textup{No, it is not possible to maintain the score.}$

Explanation:

There are five test scores. Assume and represents the student's fourth and fifth tests.

Set up an equation such that all five scores will average a 90.

$\frac{95+97+25+x+y}{5} = 90$

Multiply by five on both sides.

The equation becomes:

Isolate the x and y-variables by subtracting all the integers on both sides.

95+97+25+x+y-(95+97+25)= 450-(95+97+25)

x+y=233

Divide both sides by two to determine the average score he will need for both tests.

$\frac{x+y}{2}=\frac{233}{2} =116.5$

The student cannot maintain an average score of 90 since he will need to score a grade over 100 on both tests.

The answer is: $\textup{No, the student will not maintain the score.}$

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Example Question #74 : Mean

Determine the average of the numbers: [20,35,94,32,49]

Possible Answers:

Correct answer:

Explanation:

Add the numbers in the data set.

20+35+94+32+49= 230

Divide this value by five, since there are five numbers in the set.

$\frac{230}{5}=46$

The answer is:

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Example Question #75 : Mean

Determine the mean of the numbers: [9,18,63,75,77,-2]

Possible Answers:

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

Correct answer:

Explanation:

To determine the mean, add all the numbers and divide by the total amount of numbers given.

$\frac{9+18+63+75+77+(-2)}{6}$

Simplify the numerator.

$\frac{240}{6}=40$

The answer is:

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Example Question #79 : Mean

Determine the mean of the numbers: [5,11,26,93,100]

Possible Answers:

$\textup{There is no mean.}$

Correct answer:

Explanation:

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

Add the numbers in the data set.

5+11+26+93+100 =235

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

There are five numbers.

$\frac{235}{5}$

The answer is:

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Example Question #76 : Mean

Determine the average of the following numbers: [8,26,6,48,61,-45]

Possible Answers:

$\frac{47}{6}$

$\frac{97}{3}$

$\frac{71}{2}$

$\frac{52}{3}$

Correct answer:

$\frac{52}{3}$

Explanation:

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

Add the numbers.

8+26+6+48+61+(-45) = 104

Divide this number by six, since there are six numbers in the data set.

$\frac{104}{6}$

Reduce this fraction.

$\frac{104}{6} = \frac{52\times 2}{3\times 2} = \frac{52}{3}$

The answer is: $\frac{52}{3}$

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Algebra II : Mean

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #71 : Mean

Example Question #71 : Mean

Example Question #73 : Mean

Example Question #72 : Mean

Example Question #75 : Mean

Example Question #73 : Mean

Example Question #74 : Mean

Example Question #75 : Mean

Example Question #79 : Mean

Example Question #76 : Mean

All Algebra II Resources

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