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Algebra 1 : Statistics and Probability

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Example Questions

Example Question #146 : How To Find Median

What is the median? $[\frac{3}{8}, \frac{2}{3}, 10, \frac{5}{3}, 2]$

Possible Answers:

$\frac{3}{8}$

$\frac{5}{3}$

$\frac{2}{3}$

$\frac{3}{5}$

Correct answer:

$\frac{5}{3}$

Explanation:

The median is the central number of a chronological ordered set of numbers.

Rewrite the fractions with a least common denominator.

$[\frac{3}{8}, \frac{2}{3}, 10, \frac{5}{3}, 2]\rightarrow [\frac{9}{24},\frac{16}{24},\frac{240}{24},\frac{40}{24},\frac{48}{24}]$

The median is the third largest number.

The answer is: $\frac{5}{3}$

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Example Question #145 : How To Find Median

What is the median of the dataset: $[\frac{1}{2}, \pi, e, \sqrt5]$

Possible Answers:

$\frac{1+2\sqrt5}{4}$

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

$\textup{No median.}$

$\frac{\sqrt5+ e}{2}$

$\frac{1+2\sqrt5}{2}$

Correct answer:

$\frac{\sqrt5+ e}{2}$

Explanation:

Reorder the dataset in chronological order. Approximate each irrational number to 2 decimal places.

$\pi = 3.14$

e =2.72

$\sqrt5 = 2.24$

The least to greatest order is: $[\frac{1}{2}, \sqrt5, e, \pi]$

Since there are 4 numbers in the set, the median is the average of the center 2 numbers in the set.

The answer is: $\frac{\sqrt5+ e}{2}$

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Example Question #147 : How To Find Median

Find the median: $[1, \frac{1}{2}, \frac{1}{3}, \frac{1}{5}]$

Possible Answers:

$\frac{3}{20}$

$\frac{12}{5}$

$\frac{5}{12}$

$\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{5}{12}$

Explanation:

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

Organize the numbers from least to greatest.

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

Average the two center numbers.

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

Add the numerator.

$\frac{\frac{5}{6}}{2}$

Rewrite the complex fraction using a division sign. Use the multiplication property and take the reciprocal of the second term. Multiply the numerator with numerator and denominator with the denominator.

$\frac{5}{6} \div 2 = \frac{5}{6} \times \frac{1}{2} = \frac{5}{12}$

The answer is: $\frac{5}{12}$

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Example Question #351 : Statistics And Probability

Find the median: [-13,0,1,13]

Possible Answers:

$\textup{There is no median.}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

The given data set is already in chronological order.

The median is the average of the two numbers in the middle.

Average the center numbers.

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

The median is $\frac{1}{2}$ .

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Example Question #152 : How To Find Median

Solve for the median: [2,9,10,100]

Possible Answers:

$\frac{19}{2}$

$\textup{There is no median.}$

Correct answer:

$\frac{19}{2}$

Explanation:

The given data set is in chronological order.

Since we are given an even set of data, we will need to average the center two numbers to determine the median.

Average the center two numbers.

$\frac{9+10}{2}=\frac{19}{2}$

The median is: $\frac{19}{2}$

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Example Question #153 : How To Find Median

Solve for the median: [-2,-9,5,1]

Possible Answers:

$-\frac{1}{2}$

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

$\frac{1}{2}$

Correct answer:

$-\frac{1}{2}$

Explanation:

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

Reorder the data set.

$[-2,-9,5,1]\rightarrow [ -9,-2,1,5]$

Since there are four numbers in the data set, the median is the average of the two central numbers.

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

The median is: $-\frac{1}{2}$

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Example Question #352 : Statistics And Probability

Find the median of the data set: [-9,10,-8,7,6]

Possible Answers:

$\frac{6}{5}$

Correct answer:

Explanation:

The median of this set is the central number of the chronological ordered numbers from least to greatest.

Reorder the numbers from least to greatest.

$[-9,10,-8,7,6]\rightarrow[-9,-8,6,7,10]$

The median is .

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Example Question #155 : How To Find Median

Find the median: [-5,9,-3,10,11,12]

Possible Answers:

$\frac{17}{2}$

$\frac{17}{3}$

$\frac{19}{2}$

$\frac{7}{2}$

Correct answer:

$\frac{19}{2}$

Explanation:

To find the median, first reorganize all the numbers in chronological order.

$[-5,9,-3,10,11,12]\rightarrow [-5,-3,9,10,11,12]$

Average the center two numbers of the even number data set.

$\frac{9+10}{2} = \frac{19}{2}$

The median is: $\frac{19}{2}$

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Example Question #156 : How To Find Median

On a recent algebra test, students achieved the following scores:

Student 1:

Student 2:

Student 3:

Student 4:

Student 5:

Student 6:

Student 7:

Student 8:

Student 9:

Student 10: 100

Student 11:

What is the median score?

80, 80, 95, 90, 90, 70, 65, 85, 90, 100, 50

50, 65, 70, 80, 80, 85, 90, 90, 90, 95, 100

Possible Answers:

Correct answer:

Explanation:

The easiest way to begin this problem is to put the scores in numerical order:

50,65,70,80,80,85,90,90,90,95,100

The median is the middle score. In this case, that answer is .

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Example Question #157 : How To Find Median

Find the median of the following set of numbers:

$(2.55, 21, i^2, 56, 3.1, -55, \pi,\sqrt{2})$

where i is the imaginary number, $\sqrt{-1}$ .

Possible Answers:

5.65

2.825

2.55

0.5

3.1

Correct answer:

2.825

Explanation:

$(2.55, 21, 56, 3.1, -55, \pi,\sqrt{2} )$

First, rank the number in increasing order, remember $\pi\approx3.14$ and $ \sqrt{2}\approx 1.41 $ and $ i^2=-1$

$($ $-55, i^2, $ $\sqrt2 ,$ $2.55 ,$ $ 3.1 ,$ $\pi,21 ,$ $56)$

Since there is an even number of items in the set, the median is the averaege of the two center numbers:

Median:

(2.55+3.1)/2=2.825

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Algebra 1 : Statistics and Probability

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #146 : How To Find Median

Example Question #145 : How To Find Median

Example Question #147 : How To Find Median

Example Question #351 : Statistics And Probability

Example Question #152 : How To Find Median

Example Question #153 : How To Find Median

Example Question #352 : Statistics And Probability

Example Question #155 : How To Find Median

Example Question #156 : How To Find Median

Example Question #157 : How To Find Median

All Algebra 1 Resources

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