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Algebra II : Data Properties

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Example Questions

Example Question #289 : Basic Statistics

Determine the median of the numbers: [-3,9,-2,-1,4,-3]

Possible Answers:

$\frac{3}{2}$

$-\frac{3}{2}$

$-\frac{5}{3}$

$-\frac{5}{2}$

$\frac{2}{3}$

Correct answer:

$-\frac{3}{2}$

Explanation:

The numbers will need to be rewritten in order from least to greatest.

$[-3,9,-2,-1,4,-3] \rightarrow [-3,-3,-2,-1,4,9]$

The median of an even set of numbers is the average of the center two numbers.

$\frac{-2-1}{2} = \frac{-3}{2}$

The answer is: $-\frac{3}{2}$

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Example Question #290 : Basic Statistics

Determine the median of the following data set: [3,9,-4,-18,5,7]

Possible Answers:

$\textup{There is no median.}$

Correct answer:

Explanation:

Reorganize the numbers from least to greatest.

$[3,9,-4,-18,5,7]\rightarrow[-18,4,3,5,7,9]$

Since there is even amount of numbers provided in the set, the median is the average of the center two numbers.

Average the two numbers.

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

The answer is:

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Example Question #261 : Data Properties

Determine the median of the numbers: [ -3,9,24,-1,-16,33]

Possible Answers:

$\frac{23}{2}$

$\frac{25}{2}$

$\frac{23}{3}$

Correct answer:

Explanation:

Reorganize the numbers from least to greatest.

$[ -3,9,24,-1,-16,33]\rightarrow [-16,-3,-1,9,24,33]$

The median for an even amount of numbers in the data set is the average of the two central numbers.

Average the two numbers.

$\frac{-1+9}{2} = \frac{8}{2} =4$

The answer is:

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Example Question #262 : Data Properties

Determine the median: [-3,-9,27,18]

Possible Answers:

$\textup{There is no median.}$

$\frac{57}{4}$

$\frac{27}{2}$

$\frac{33}{4}$

$\frac{15}{2}$

Correct answer:

$\frac{15}{2}$

Explanation:

Reorder the numbers from least to greatest.

$[-3,-9,27,18]\rightarrow [ -9,-3,18,27]$

The median of an even set of data is the average of the center two numbers in a chronological ordered set of numbers.

Average the two numbers.

$\frac{-3+18}{2} = \frac{15}{2}$

The answer is: $\frac{15}{2}$

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Example Question #263 : Data Properties

Determine the median: $[2,i,e, \pi, 30]$

Possible Answers:

$\frac{e}{2}$

$\frac{\pi+e}{2}$

$\textup{Cannot be determined.}$

Correct answer:

$\textup{Cannot be determined.}$

Explanation:

The median is defined as the central number of a given set of numbers. We have two real numbers and two irrational numbers. However, notice that there is an imaginary term given in the data set.

$i=\sqrt{-1}$

This value is undefined and is not a real number. We cannot reorder the data set in chronological order and the median is unknown.

The answer is: $\textup{Cannot be determined.}$

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Example Question #264 : Data Properties

Determine the median: [9,-3,28,0]

Possible Answers:

$-\frac{3}2$

$\frac{9}{2}$

$\frac{25}{2}$

$\textup{There is no median.}$

$\frac{17}{2}$

Correct answer:

$\frac{9}{2}$

Explanation:

The median of a set of even numbers is the average of the central two numbers in a least to greatest ordered set.

Arrange the numbers from least to greatest.

$[9,-3,28,0]\rightarrow [ -3,0,9,28]$

Average the center two numbers.

The answer is: $\frac{9}{2}$

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Example Question #291 : Basic Statistics

What is the median of the following numbers? [0,-9,8,-7,3,39]

Possible Answers:

$\frac{1}{2}$

$\frac{3}{2}$

$\textup{The median cannot be determined.}$

$\frac{17}{3}$

Correct answer:

$\frac{3}{2}$

Explanation:

Reorganize the data set in chronological order.

$[0,-9,8,-7,3,39]\rightarrow [-9,-7,0,3,8,39]$

The median is the average of the 2 central numbers in an even set of data.

Average the two numbers.

$\frac{0+3}{2} = \frac{3}{2}$

The answer is: $\frac{3}{2}$

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Example Question #266 : Data Properties

Determine the median of the set of numbers: [-5,-8,36,52]

Possible Answers:

$\frac{101}{2}$

$\frac{75}{4}$

$\frac{31}{2}$

$\textup{There is no median.}$

Correct answer:

$\frac{31}{2}$

Explanation:

Rearrange the numbers from least to greatest.

$[-5,-8,36,52]\rightarrow [-8,-5,36,52]$

The median of an even set of numbers is the average of the center two numbers in the data set.

Average the two numbers.

$\frac{-5+36}{2}= \frac{31}{2}$

The answer is: $\frac{31}{2}$

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Example Question #267 : Data Properties

Determine the median of the following set of numbers:

[-2,-8,16,-32,13,7]

Possible Answers:

$\frac{5}{2}$

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

$-\frac{9}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

In order to determine the median, first we will need to rearrange the numbers from least to greatest.

$[-2,-8,16,-32,13,7]\rightarrow [-32,-8,-2,7,13,16]$

The median of an even numbered set of numbers is the average of the central two numbers in the data set.

Average the two numbers.

$\frac{-2+7}{2} = \frac{5}{2}$

The median is: $\frac{5}{2}$

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Example Question #268 : Data Properties

Determine the median of the numbers: [-4,3,-2,-8,0,1]

Possible Answers:

$\textup{There is no median.}$

$-\frac{5}{3}$

Correct answer:

Explanation:

Reorganize the data set in chronological order from least to greatest.

$[-4,3,-2,-8,0,1]\rightarrow [-8,-4,-2,0,1,3]$

The median of an even set of data is the average of the two central numbers of an ordered set.

Average the two numbers.

$\frac{(-2)+0}{2} = -1$

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 #289 : Basic Statistics

Example Question #290 : Basic Statistics

Example Question #261 : Data Properties

Example Question #262 : Data Properties

Example Question #263 : Data Properties

Example Question #264 : Data Properties

Example Question #291 : Basic Statistics

Example Question #266 : Data Properties

Example Question #267 : Data Properties

Example Question #268 : Data Properties

All Algebra II Resources

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