Algebra II : Data Properties

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #356 : Algebra Ii

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

Possible Answers:

\displaystyle -\frac{3}{2}

\displaystyle \frac{3}{2}

\displaystyle -\frac{5}{2}

\displaystyle \frac{2}{3}

\displaystyle -\frac{5}{3}

Correct answer:

\displaystyle -\frac{3}{2}

Explanation:

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

\displaystyle [-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.

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

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

Example Question #282 : Basic Statistics

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

Possible Answers:

\displaystyle 8

\displaystyle 4

\displaystyle -9

\displaystyle -11

Correct answer:

\displaystyle 4

Explanation:

Reorganize the numbers from least to greatest.

\displaystyle [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.

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

The answer is:  \displaystyle 4

Example Question #361 : Algebra Ii

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

Possible Answers:

\displaystyle \frac{25}{2}

\displaystyle 4

\displaystyle \frac{23}{3}

\displaystyle 8

\displaystyle \frac{23}{2}

Correct answer:

\displaystyle 4

Explanation:

Reorganize the numbers from least to greatest.

\displaystyle [ -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.

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

The answer is:  \displaystyle 4

Example Question #261 : Data Properties

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

Possible Answers:

\displaystyle \frac{15}{2}

\displaystyle \frac{27}{2}

\displaystyle \frac{33}{4}

\displaystyle \frac{57}{4}

Correct answer:

\displaystyle \frac{15}{2}

Explanation:

Reorder the numbers from least to greatest.

\displaystyle [-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.

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

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

Example Question #263 : Data Properties

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

Possible Answers:

\displaystyle \frac{e}{2}

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

 

\displaystyle i

\displaystyle e

Correct answer:

 

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.  

\displaystyle 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:  

Example Question #361 : Algebra Ii

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

Possible Answers:

\displaystyle \frac{25}{2}

\displaystyle \frac{17}{2}

\displaystyle -\frac{3}2

\displaystyle \frac{9}{2}

Correct answer:

\displaystyle \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.

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

Average the center two numbers.

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

Example Question #291 : Basic Statistics

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

Possible Answers:

\displaystyle \frac{17}{3}

\displaystyle 8

\displaystyle \frac{3}{2}

\displaystyle \frac{1}{2}

Correct answer:

\displaystyle \frac{3}{2}

Explanation:

Reorganize the data set in chronological order.

\displaystyle [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.

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

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

Example Question #361 : Algebra Ii

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

Possible Answers:

\displaystyle \frac{31}{2}

\displaystyle 14

\displaystyle \frac{101}{2}

\displaystyle \frac{75}{4}

Correct answer:

\displaystyle \frac{31}{2}

Explanation:

Rearrange the numbers from least to greatest.

\displaystyle [-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.

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

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

Example Question #261 : Data Properties

Determine the median of the following set of numbers:  

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

Possible Answers:

\displaystyle \frac{5}{2}

\displaystyle -1

\displaystyle 10

\displaystyle -\frac{9}{2}

Correct answer:

\displaystyle \frac{5}{2}

Explanation:

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

\displaystyle [-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.

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

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

Example Question #268 : Data Properties

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

Possible Answers:

\displaystyle 5

\displaystyle -\frac{5}{3}

\displaystyle -1

\displaystyle -5

Correct answer:

\displaystyle -1

Explanation:

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

\displaystyle [-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.

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

The answer is:  \displaystyle -1

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