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Algebra 1 : How to find median

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Example Questions

Example Question #151 : How To Find Median

Find the median: $\displaystyle [-13,0,1,13]$

Possible Answers:

$\displaystyle 1$

$\textup{There is no median.}$ $\displaystyle \textup{There is no median.}$

$\displaystyle 0$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 13$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

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.

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

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

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Example Question #152 : How To Find Median

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

Possible Answers:

$\displaystyle 32$

$\displaystyle 10$

$\displaystyle 51$

$\frac{19}{2}$ $\displaystyle \frac{19}{2}$

$\textup{There is no median.}$ $\displaystyle \textup{There is no median.}$

Correct answer:

$\frac{19}{2}$ $\displaystyle \frac{19}{2}$

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.

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

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

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Example Question #153 : How To Find Median

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

Possible Answers:

$\displaystyle -2$

$\displaystyle -7$

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

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

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

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

Explanation:

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

Reorder the data set.

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

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

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

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

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Example Question #154 : How To Find Median

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

Possible Answers:

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

$\displaystyle -8$

$\displaystyle 6$

$\displaystyle 7$

$\displaystyle -9$

Correct answer:

$\displaystyle 6$

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.

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

The median is $\displaystyle 6$.

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Example Question #155 : How To Find Median

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

Possible Answers:

$\frac{17}{3}$ $\displaystyle \frac{17}{3}$

$\frac{19}{2}$ $\displaystyle \frac{19}{2}$

$\displaystyle 9$

$\frac{7}{2}$ $\displaystyle \frac{7}{2}$

$\frac{17}{2}$ $\displaystyle \frac{17}{2}$

Correct answer:

$\frac{19}{2}$ $\displaystyle \frac{19}{2}$

Explanation:

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

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

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

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

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

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Example Question #356 : Statistics And Probability

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

Student 1: $\displaystyle 80$

Student 2: $\displaystyle 80$

Student 3: $\displaystyle 95$

Student 4: $\displaystyle 90$

Student 5: $\displaystyle 90$

Student 6: $\displaystyle 70$

Student 7: $\displaystyle 65$

Student 8: $\displaystyle 85$

Student 9: $\displaystyle 90$

Student 10: 100 $\displaystyle 100$

Student 11: $\displaystyle 50$

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:

$\displaystyle 90$

$\displaystyle 85$

$\displaystyle 50$

$\displaystyle 81$

$\displaystyle 80$

Correct answer:

$\displaystyle 85$

Explanation:

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

$\displaystyle 50,65,70,80,80,85,90,90,90,95,100$

The median is the middle score. In this case, that answer is $\displaystyle 85$.

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Example Question #156 : How To Find Median

Find the median of the following set of numbers:

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

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

Possible Answers:

3.1 $\displaystyle 3.1$

0.5 $\displaystyle 0.5$

2.825 $\displaystyle 2.825$

5.65 $\displaystyle 5.65$

2.55 $\displaystyle 2.55$

Correct answer:

2.825 $\displaystyle 2.825$

Explanation:

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

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

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

$\displaystyle (2.55+3.1)/2=2.825$

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Example Question #157 : How To Find Median

Find the median of the following data set:

23, 24, 26, 32, 31, 32, 22, 21, 20, 30

Possible Answers:

26.1

Correct answer:

Explanation:

List the values in numerical order:

20, 21, 22, 23, 24, 26, 30, 31, 32, 32

Find the middle two numbers:

24, 26

Find the average of the middle numbers by adding them and dividing by 2:

$\displaystyle 24+26 = 50$

$50\div 2 = 25$ $\displaystyle 50\div 2 = 25$

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Algebra 1 : How to find median

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #151 : How To Find Median

Example Question #152 : How To Find Median

Example Question #153 : How To Find Median

Example Question #154 : How To Find Median

Example Question #155 : How To Find Median

Example Question #356 : Statistics And Probability

Example Question #156 : How To Find Median

Example Question #157 : How To Find Median

All Algebra 1 Resources

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