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Algebra II : Median

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Example Question #51 : Median

Determine the median of the following numbers: [0,6,18,24,36,48]

Possible Answers:

Correct answer:

Explanation:

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

The center two numbers are 18 and 24 since the set is already in chronological order.

Average the two numbers.

$\frac{18+24}{2} = \frac{42}{2} = 21$

The median is .

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Example Question #51 : Median

Determine the median: $[-1, -3, \frac{1}{2}, 0, -8 , 9, 20]$

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{5}{2}$

Correct answer:

Explanation:

Reorder the data set in chronological order.

$[-1, -3, \frac{1}{2}, 0, -8 , 9, 20]\rightarrow [ -8,-3,-1,0,\frac{1}{2},9,20]$

The median of an odd set of numbers is the central number of the data set.

Do not average the numbers.

The median is:

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Example Question #53 : Median

Determine the median of the following numbers: $[0,\frac{1}{9},\frac{1}{18},\frac{1}{6}]$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{12}$

$\frac{5}{18}$

$\frac{1}{3}$

$\frac{5}{36}$

Correct answer:

$\frac{1}{12}$

Explanation:

The numbers are not in chronological order. Rewrite all fractions with the least common denominator.

$[0,\frac{1}{9},\frac{1}{18},\frac{1}{6}]\rightarrow[0,\frac{1(2)}{9(2)}, \frac{1}{18}, \frac{1(3)}{6(3)}]\rightarrow [0,\frac{2}{18},\frac{1}{18}, \frac{3}{18}]$

Comparing the numerators, we can sort the numbers from least to greatest.

$[0,\frac{1}{18},\frac{2}{18}, \frac{3}{18}]$

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

$\frac{\frac{1}{18}+\frac{2}{18}}{2} = \frac{\frac{3}{18}}{2} = \frac{\frac{1}{6}}{2}$

Simplify the complex fraction.

$\frac{1}{6} \div 2 = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}$

The answer is: $\frac{1}{12}$

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Example Question #54 : Median

Determine the median of the numbers: [-1,-3,1,0,1,10]

Possible Answers:

$\frac{7}{3}$

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{4}{3}$

Correct answer:

$\frac{1}{2}$

Explanation:

In order to determine the median, we will need to rearrange the data set from least to greatest.

$[-1,-3,1,0,1,10]\rightarrow[-3,-1,0,1,1,10]$

Since there is an even amount of numbers, the median is the average of the two central numbers.

$\frac{0+1}{2} = \frac{1}{2}$

The answer is: $\frac{1}{2}$

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Example Question #55 : Median

Determine the median of the data set: [9,36,47,-3]

Possible Answers:

$\frac{45}{2}$

$\frac{83}{2}$

$\frac{89}{4}$

$\frac{13}{4}$

Correct answer:

$\frac{45}{2}$

Explanation:

Reorder the numbers in chronological order from least to greatest.

$[9,36,47,-3]\rightarrow[-3,9,36,47]$

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

Average the two numbers.

$\frac{36+9}{2}= \frac{45}{2}$

The answer is: $\frac{45}{2}$

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Example Question #56 : Median

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

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

$-\frac{5}{3}$

$\frac{2}{3}$

$-\frac{5}{2}$

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 #57 : Median

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 #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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Algebra II : Median

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #51 : Median

Example Question #51 : Median

Example Question #53 : Median

Example Question #54 : Median

Example Question #55 : Median

Example Question #56 : Median

Example Question #57 : Median

Example Question #58 : Median

Example Question #59 : Median

Example Question #60 : Median

All Algebra II Resources

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