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Algebra II : Median

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Example Question #71 : Median

Determine the median: [-3,9,-5,0,-33,-77,23]

Possible Answers:

$-\frac{86}{7}$

100

Correct answer:

Explanation:

Organize the data set from least to greatest.

$[-3,9,-5,0,-33,-77,23]\rightarrow[-77,-33,-5,-3,0,9,23]$

The median is the central number in an odd number of numbers provided.

The answer is:

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Example Question #72 : Median

Determine the median: [-9,30,5,-7]

Possible Answers:

$\textup{There is no median.}$

$\frac{35}{2}$

Correct answer:

Explanation:

The median is the center number of a data set. However, since we have an even number of numbers given, we will need to arrange the set from least to greatest, and average the central two numbers.

Reorganize the numbers from least to greatest.

$[-9,30,5,-7] \rightarrow [ -9,-7,5,30]$

Average the two center numbers in the data set.

$\frac{-7+5}{2} = \frac{-2}{2}=-1$

The answer is:

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Example Question #73 : Median

Determine the median: [ -6,33,-8,50]

Possible Answers:

$\frac{25}{2}$

$\frac{41}{2}$

$\textup{There is no median.}$

$\frac{27}{2}$

$-\frac{41}{2}$

Correct answer:

$\frac{27}{2}$

Explanation:

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

$[ -6,33,-8,50] \rightarrow [-8,-6,33,50]$

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

Average the two numbers.

$\frac{-6+33}{2} = \frac{27}{2}$

The answer is: $\frac{27}{2}$

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Example Question #74 : Median

Determine the median of the numbers: [2,66,84,95]

Possible Answers:

$\frac{247}{2}$

$\frac{147}{2}$

$\textup{There is no median.}$

$\frac{97}{2}$

Correct answer:

Explanation:

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

The set is already in order from least to greatest.

Average the two center numbers.

$\frac{66+84}{2} = 75$

The answer is:

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Example Question #75 : Median

Determine the median: [-9,3,-9,18,-9,8]

Possible Answers:

$\frac{9}{2}$

Correct answer:

Explanation:

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

Rearrange the numbers from least to greatest.

$[-9,3,-9,18,-9,8] \rightarrow [ -9,-9,-9,3,8,18]$

Average the center two numbers.

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

The answer is:

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Example Question #76 : Median

Determine the median: [-9,-9,-8,13,27,61]

Possible Answers:

$\textup{There is no median.}$

$\frac{25}{3}$

$\frac{21}{2}$

$\frac{25}{2}$

$\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

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

The set of numbers are already from least to greatest.

Average the two center numbers.

$\frac{-8+13}{2} = \frac{5}{2}$

The median is: $\frac{5}{2}$

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Example Question #77 : Median

Determine the median of the numbers: [-5,11,-9,-15]

Possible Answers:

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

Correct answer:

Explanation:

Reorganize all the numbers from least to greatest.

$[-5,11,-9,-15]\rightarrow [-15,-9,-5,11]$

The median for an even amount of numbers in the data set is the average of the two central numbers.

Average the two numbers.

$\frac{-9+(-5)}{2} = \frac{-14}{2} = -7$

The median is:

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Example Question #78 : Median

Most chess tournaments use a rating system called Elo, which is named after a physics professor named Arpad Elo who developed the rating system. The 2014 Sinquefield Cup was a tournament in which the elite chess players of the world competed. Below is a list of their Elo ratings.

Sinquefield

Find the median Elo rating of the players participating in the 2014 Sinquefield Cup.

Possible Answers:

4.5

2794

2772

2802

2768

Correct answer:

2794

Explanation:

Step 1:

To make this problem easier to solve, let's list out the Elo ratings from least to greatest.

Step 2:

Because there are an even amount of players, there will be two middle terms. We must take the average of the two middle terms in order to get an accurate median value.

2794

Solution:

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Example Question #72 : Median

Find the median of the data.

$\{1,85,3,8,54,21,46,3,154\}$

Possible Answers:

41.67

Correct answer:

Explanation:

The median in the number in the middle of the data set.

Arrange the data in numerical order.

$\{1,85,3,8,54,21,46,3,154\}\rightarrow$ $\{1,3,3,8,{\color{Red} 21},46,54,85,154\}$ .

Therefore, the median is 21.

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Example Question #80 : Median

Give the median of the following data:

12, 43, 50, 83, 59, 23, 20, 42, 95, 59, 20

Possible Answers:

506

and

Correct answer:

Explanation:

The correct answer is . It is regarded as the middle value, or the average of the two middle values of a data set. The first step in finding the median is ordering the data from least to greatest.

12, 20, 20, 23, 42, 43, 50, 59, 59, 83, 95

From here, find the middle value. In this case, that is the ^th value, .

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Algebra II : Median

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #71 : Median

Example Question #72 : Median

Example Question #73 : Median

Example Question #74 : Median

Example Question #75 : Median

Example Question #76 : Median

Example Question #77 : Median

Example Question #78 : Median

Example Question #72 : Median

Example Question #80 : Median

All Algebra II Resources

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