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Algebra II : Basic Statistics

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Example Questions

Example Question #58 : Median

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

Possible Answers:

$\frac{25}{2}$

$\frac{23}{3}$

$\frac{23}{2}$

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 #59 : Median

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

Possible Answers:

$\frac{15}{2}$

$\frac{27}{2}$

$\textup{There is no median.}$

$\frac{33}{4}$

$\frac{57}{4}$

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 #60 : Median

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

Possible Answers:

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

$\frac{e}{2}$

$\textup{Cannot be determined.}$

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 #61 : Median

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

Possible Answers:

$\frac{17}{2}$

$-\frac{3}2$

$\frac{25}{2}$

$\textup{There is no median.}$

$\frac{9}{2}$

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 #62 : Median

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

Possible Answers:

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

$\frac{17}{3}$

$\frac{3}{2}$

$\frac{1}{2}$

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 #63 : Median

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

Possible Answers:

$\frac{101}{2}$

$\frac{31}{2}$

$\textup{There is no median.}$

$\frac{75}{4}$

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 #64 : Median

Determine the median of the following set of numbers:

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

Possible Answers:

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

$\frac{5}{2}$

$-\frac{9}{2}$

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 #65 : Median

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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Example Question #66 : Median

Determine the median of the numbers: [5,-5,9,0,-3,6,7,8]

Possible Answers:

$\frac{27}{8}$

$\textup{There is no median.}$

$-\frac{3}{2}$

$\frac{11}{2}$

Correct answer:

$\frac{11}{2}$

Explanation:

Organize the numbers from least to greatest.

$[5,-5,9,0,-3,6,7,8]\rightarrow[-5,-3,0,5,6,7,8,9]$

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

Average the two numbers.

$\frac{5+6}{2} =\frac{11}{2}$

The answer is: $\frac{11}{2}$

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Example Question #67 : Median

Determine the median: [-1,-8,30,52]

Possible Answers:

$\frac{73}{4}$

$\frac{31}{2}$

$\textup{There is no median.}$

$\frac{29}{2}$

Correct answer:

$\frac{29}{2}$

Explanation:

The median of an even numbered set of data is the average of the two central numbers in an ordered data set from least to greatest.

Rearrange the numbers so that it's from least to greatest.

$[-1,-8,30,52]\rightarrow[ -8,-1,30,52]$

Average the two central numbers.

$\frac{(-1)+30}{2} = \frac{29}{2}$

The answer is: $\frac{29}{2}$

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Algebra II : Basic Statistics

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #58 : Median

Example Question #59 : Median

Example Question #60 : Median

Example Question #61 : Median

Example Question #62 : Median

Example Question #63 : Median

Example Question #64 : Median

Example Question #65 : Median

Example Question #66 : Median

Example Question #67 : Median

All Algebra II Resources

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