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Algebra II : Basic Statistics

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Example Questions

Example Question #41 : Mean

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 #49 : Mean

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:

7.69

8.67

8.04

7.98

8.24

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 #50 : 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 #51 : Mean

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

Possible Answers:

$\frac{14}{5}$

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

$\frac{24}{5}$

$\frac{8}{5}$

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 #52 : Mean

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

Possible Answers:

1.275

1.0275

0.55

1.025

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 #53 : Mean

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

Possible Answers:

$\frac{37}{120}$

$\frac{59}{240}$

$\frac{269}{240}$

$\frac{29}{240}$

$\frac{47}{120}$

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 #54 : Mean

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

Possible Answers:

$\textup{There is no mean.}$

$\frac{5}{2}$

$-\frac{13}{2}$

$\frac{13}{2}$

$-\frac{1}{2}$

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 #55 : Mean

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

Possible Answers:

$\frac{323}{6}$

$\frac{79}{2}$

$\frac{313}{6}$

$\frac{101}{2}$

$\textup{There is no mean.}$

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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Example Question #151 : Data Properties

Find the mean of the following data set. [-1,-5,-8,17,41]

Possible Answers:

$-\frac{49}{5}$

$\frac{49}{5}$

$\frac{22}{5}$

$\frac{44}{5}$

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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Algebra II : Basic Statistics

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Mean

Example Question #49 : Mean

Example Question #50 : Mean

Example Question #51 : Mean

Example Question #52 : Mean

Example Question #53 : Mean

Example Question #54 : Mean

Example Question #55 : Mean

Example Question #56 : Mean

Example Question #151 : Data Properties

All Algebra II Resources

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