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Algebra II : Data Properties

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Example Questions

Example Question #41 : Median

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

Possible Answers:

$\frac{17}{24}$

$\frac{1}{2}$

$\frac{11}{24}$

$\frac{3}{8}$

$\frac{5}{6}$

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 #42 : 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 #281 : Basic Statistics

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

Possible Answers:

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

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

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

$\textup{There is no median.}$

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

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 #43 : 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 #44 : Median

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

Possible Answers:

1.87

2.5

1.6

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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Example Question #284 : Basic Statistics

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 #285 : Basic Statistics

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

Possible Answers:

$\frac{5}{2}$

$\frac{1}{2}$

$-\frac{1}{2}$

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 #281 : Basic Statistics

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

Possible Answers:

$\frac{1}{12}$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{5}{18}$

$\frac{5}{36}$

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 #251 : Data Properties

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

Possible Answers:

$\frac{4}{3}$

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{7}{3}$

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 #288 : Basic Statistics

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

Possible Answers:

$\frac{89}{4}$

$\frac{13}{4}$

$\frac{45}{2}$

$\frac{83}{2}$

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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Algebra II : Data Properties

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Median

Example Question #42 : Median

Example Question #281 : Basic Statistics

Example Question #43 : Median

Example Question #44 : Median

Example Question #284 : Basic Statistics

Example Question #285 : Basic Statistics

Example Question #281 : Basic Statistics

Example Question #251 : Data Properties

Example Question #288 : Basic Statistics

All Algebra II Resources

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