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Algebra II : Median

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Example Question #41 : Median

Find the median of the data set: [-3,9,10,-6]

Possible Answers:

$\frac{19}{2}$

$\frac{15}{2}$

$\frac{-9}{2}$

$\textup{There is no median.}$

Correct answer:

Explanation:

The median is the central number of a chronological ordered data set from least to greatest.

Reorder the data set from least to greatest.

$[-3,9,10,-6]\rightarrow[-6,-3,9,10]$

Since there are four numbers provided, the median is the average of the second and third numbers.

Average the two numbers.

$\frac{-3+9}{2} = \frac{6}{2}=3$

The median is:

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Example Question #42 : Median

Solve for the median: $[-\frac{1}{2}, -\frac{2}{5}, 3,-3]$

Possible Answers:

$\frac{9}{40}$

$\frac{13}{5}$

$-\frac{9}{20}$

$-\frac{9}{40}$

$-\frac{3}{10}$

Correct answer:

$-\frac{9}{20}$

Explanation:

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

Negative half is less than negative two-fifth.

$[-\frac{1}{2}, -\frac{2}{5}, 3,-3] \rightarrow[-3,-\frac{1}{2}, -\frac{2}{5}, 3]$

Since this is an even number set of numbers, the median is the average of the middle two numbers.

Average the two fractions.

$\frac{-\frac{1}{2}+ (-\frac{2}{5})}{2} = \frac{-\frac{5}{10}-\frac{4}{10}}{2}= \frac{-\frac{9}{10}}{2}$

Rewrite the complex fraction using a division sign.

$\frac{-\frac{9}{10}}{2} = -\frac{9}{10} \div 2$

Change the division sign to multiplication and take the reciprocal of the second number.

$-\frac{9}{10} \times\frac{1}{2} = -\frac{9}{20}$

The median is: $-\frac{9}{20}$

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Example Question #43 : Median

Solve for the median: $[\frac{17}{3}, \frac{5}{2},\frac{3}{4}, \frac{1}{10}]$

Possible Answers:

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

$\frac{49}{12}$

$\frac{13}{8}$

$\frac{17}{40}$

$\frac{541}{240}$

Correct answer:

$\frac{13}{8}$

Explanation:

The median of an even number set is the average of the center two numbers in a chronological ordered set from least to greatest.

To arrange the data set, we will need to compare numerators of the similar denominator.

Find the least common denominator. The least common denominator is since it is the minimum number divisible by all of the existing denominators.

Convert all fractions to the common denominator.

$[\frac{17}{3}, \frac{5}{2},\frac{3}{4}, \frac{1}{10}]\rightarrow [\frac{17(20)}{3(20)}, \frac{5(30)}{2(30)},\frac{3(15)}{4(15)}, \frac{1(6)}{10(6)}]$

The data set becomes: $[\frac{340}{60}, \frac{150}{60}, \frac{45}{60}, \frac{6}{60}]$

We can now see that the middle two numbers are: $\frac{5}{2},\frac{3}{4}$

Average these two numbers.

$\frac{1}{2}[\frac{5}{2}+\frac{3}{4}] = \frac{1}{2}[\frac{10}{4}+\frac{3}{4}] =\frac{1}{2}[\frac{13}{4}]$

The answer is: $\frac{13}{8}$

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Example Question #44 : Median

Solve for the median: [9,9,1,1,9,1]

Possible Answers:

$\textup{There is no median.}$

Correct answer:

Explanation:

In order to solve for the median, we will need to rearrange the data set in chronological order from least to greatest.

$[9,9,1,1,9,1]\rightarrow[1,1,1,9,9,9]$

In an even set of data, the median is the average of the central two numbers.

Average the center two numbers.

$\frac{1+9}{2}= \frac{10}{2}=5$

The median is:

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Example Question #45 : Median

Solve for the median: $[\frac{2}{5},\frac{1}{2}, \frac{3}{8}, 1]$

Possible Answers:

$\frac{7}{16}$

$\textup{There is no median.}$

$\frac{9}{40}$

$\frac{7}{8}$

$\frac{9}{20}$

Correct answer:

$\frac{9}{20}$

Explanation:

The numbers not in chronological order.

Change the fractions and the integer to a common denominator. The common denominator of the fractions is since this is the least number that is divisible by each of the denominators given.

Convert the fractions.

$[\frac{2}{5},\frac{1}{2}, \frac{3}{8}, 1]\rightarrow [\frac{16}{40},\frac{20}{40},\frac{15}{40},\frac{40}{40}]$

The median of an even data set is the mean of the center two numbers in a chronological ordered data set from least to greatest.

$[\frac{15}{40},\frac{16}{40},\frac{20}{40},\frac{40}{40}]$

The central numbers are $\frac{16}{40}$ and $\frac{20}{40}$ .

Average these numbers.

$\frac{1}{2}(\frac{16}{40}+\frac{20}{40}) = \frac{1}{2}(\frac{36}{40}) = \frac{18}{40} =\frac{9}{20}$

The answer is: $\frac{9}{20}$

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Example Question #46 : Median

Solve for the median: $[\frac{2}{3}, 0, \frac{3}{4},1]$

Possible Answers:

$\frac{17}{24}$

$\frac{3}{8}$

$\frac{5}{6}$

$\frac{11}{24}$

$\frac{1}{2}$

Correct answer:

$\frac{17}{24}$

Explanation:

Reorder the data set from least to greatest.

$[\frac{2}{3}, 0, \frac{3}{4},1]\rightarrow [0,\frac{2}{3},\frac{3}{4},1]$

The median in an odd set of numbers will the average of the two central numbers given.

Average the two center numbers.

$\frac{1}{2}[\frac{2}{3}+\frac{3}{4}]=\frac{1}{2}[\frac{8}{12}+\frac{9}{12}] = \frac{1}{2}[\frac{17}{12}]$

The answer is: $\frac{17}{24}$

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Example Question #47 : Median

Determine the median: [1,3,2,9,8,7,5,35]

Possible Answers:

$\frac{35}{3}$

Correct answer:

Explanation:

The data set provided is not in chronological order.

Reorder the set from least to greatest.

$[1,3,2,9,8,7,5,35]\rightarrow[1,2,3,5,7,8,9,35]$

Since this an even numbered data set, we will need need to average the two center numbers to find the median.

$\frac{5+7}{2}=\frac{12}{2}=6$

The median is:

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Example Question #48 : Median

Determine the median: $[\pi, e, -1,\sqrt2]$

Possible Answers:

$\frac{\sqrt2 +\pi}{2}$

$\frac{\sqrt2+e}{2}$

$\textup{There is no median.}$

$\frac{e-1}{2}$

$\frac{\sqrt{2e}}{2}$

Correct answer:

$\frac{\sqrt2+e}{2}$

Explanation:

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

Rewrite all the irrational numbers in decimal and reorder.

$[\pi=3.142, e= 2.718, -1,\sqrt2 = 1.414]\rightarrow [-1,\sqrt2,e,\pi]$

The median of an even numbered data set will the average the middle two numbers.

The answer is: $\frac{\sqrt2+e}{2}$

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Example Question #49 : Median

Determine the median: [2,9,5,3,6,7]

Possible Answers:

$\frac{11}{2}$

$\frac{16}{3}$

$\textup{There is no median.}$

Correct answer:

$\frac{11}{2}$

Explanation:

Reorder the data set in chronological order.

$[2,9,5,3,6,7]\rightarrow[2,3,5,6,7,9]$

Average the two center numbers, since this data set has an even numbered set of data.

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

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

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Example Question #251 : Data Properties

Determine the median of the data set: [0.01,0.2,3,5,3,0]

Possible Answers:

1.87

1.6

2.5

Correct answer:

1.6

Explanation:

Rearrange the data set from least to greatest.

$[0.01,0.2,3,5,3,0]\rightarrow[0,0.01,0.2,3,3,5]$

Since we have six numbers in the data set, the median is the average of the center two numbers.

Average the two numbers.

$\frac{0.2+3}{2} = \frac{3.2}{2} = 1.6$

The median is: 1.6

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Algebra II : Median

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Median

Example Question #42 : Median

Example Question #43 : Median

Example Question #44 : Median

Example Question #45 : Median

Example Question #46 : Median

Example Question #47 : Median

Example Question #48 : Median

Example Question #49 : Median

Example Question #251 : Data Properties

All Algebra II Resources

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