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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #241 : Algebra Ii

A school district has determined that the most vaulable way to evaluate success is by using the mean of all the test scores as the basis. With this in mind, find the mean scores of 77, 80, 35, 76, 99, 95, 86, 65, 72, 56, and 21?

Possible Answers:

$\small 72$

$\small 69$

$\small 66$

$\small 70$

$\small 68$

Correct answer:

$\small 69$

Explanation:

Here you need to add up all the numbers and then divide by the total number of numbers present.

So:

$\small \frac{(77+80+35+76+99+95+86+65+72+56+21)}{11}$

$\small =69$

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Example Question #171 : Basic Statistics

What is the mean of the function $f(x)= \frac{x^2 +x}{2}$ for (x=1, 2, 4, 6) ?

Possible Answers:

$\frac{35}{4}$

$\frac{13}{4}$

Correct answer:

$\frac{35}{4}$

Explanation:

To find the mean, first we need to solve the function for each of the variables given:

$f(1)= \frac{(1)^2 +(1)}{2}=1$

$f(2)= \frac{(2)^2 +(2)}{2}=3$

$f(4)= \frac{(4)^2 +(4)}{2}=10$

$f(6)= \frac{(6)^2 +(6)}{2} =21$

Then we add the numbers up and divide by how many numbers there were:

$mean = \frac{1+3+10+21}{4}$

$mean = \frac{35}{4}$

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Example Question #172 : Basic Statistics

Judges in a diving competition give a diver scores of 8.7 , 9.2 , 7.8 , 8.3 , and 7.2 . What is the mean of the scores?

Possible Answers:

8.24

7.98

8.67

8.04

7.69

Correct answer:

8.24

Explanation:

To find the mean, first we're going to add all the scores:

8.7+9.2+7.8+8.3+7.2=41.2

Next, we divide that by the number of scores we had:

$\frac{41.2}{5}=8.24$

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Example Question #44 : Mean

In the data set $x=\left \{ 2,5,3,6,N\right \}$ , what would have to be to make the mean equal ?

Possible Answers:

Correct answer:

Explanation:

In order to find the mean, we would first add all the numbers up and divide by how many numbers we have. Though we don't yet know the value for , we do know the mean.

$mean = \frac{sum}{count}$

$4=\frac{2+5+3+6+N}{5}$

From here we can clear the denominator by multiplying each side by , and we can do most of the addition:

20=16+N

Now solving for :

N=4

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Example Question #174 : Basic Statistics

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

Possible Answers:

$\frac{14}{5}$

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

$\frac{8}{5}$

$\frac{24}{5}$

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 #51 : Mean

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

Possible Answers:

1.0275

1.025

0.55

1.275

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 #176 : Basic Statistics

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

Possible Answers:

$\frac{269}{240}$

$\frac{37}{120}$

$\frac{47}{120}$

$\frac{59}{240}$

$\frac{29}{240}$

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 #177 : Basic Statistics

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

Possible Answers:

$-\frac{13}{2}$

$\frac{13}{2}$

$-\frac{1}{2}$

$\textup{There is no mean.}$

$\frac{5}{2}$

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 #178 : Basic Statistics

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

Possible Answers:

$\frac{323}{6}$

$\frac{101}{2}$

$\frac{313}{6}$

$\frac{79}{2}$

$\textup{There is no mean.}$

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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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #241 : Algebra Ii

Example Question #171 : Basic Statistics

Example Question #172 : Basic Statistics

Example Question #44 : Mean

Example Question #174 : Basic Statistics

Example Question #51 : Mean

Example Question #176 : Basic Statistics

Example Question #177 : Basic Statistics

Example Question #178 : Basic Statistics

Example Question #56 : Mean

All Algebra II Resources

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