To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set. So, given the set

\(\displaystyle 84, 76, 81, 88, 91, 85, 76, 90, 80\)

we will arrange the numbers in ascending order (from smallest to largest). We get

\(\displaystyle 76, 76, 80, 81, 84, 85, 88, 90, 91\)

Now, we will find the number in the middle of the set.

\(\displaystyle 76, 76, 80, 81, {\color{Red} 84}, 85, 88, 90, 91\)

Therefore, the median of the data set is 84. 

Reorder the numbers from least to greatest.

\(\displaystyle [-5,13,-21,-12] \rightarrow [-21,-12,-5,13]\)

The median is the average of the central numbers of an ordered set of numbers.

\(\displaystyle \frac{-12+(-5)}{2} = \frac{-17}{2} =- \frac{17}{2}\)

The answer is:  \(\displaystyle - \frac{17}{2}\)

Rewrite the data set from least to greatest.

\(\displaystyle [5,-6,-7,14] \rightarrow [-7,-6,5,14]\)

Average the central two numbers.

\(\displaystyle \frac{-6+5}{2} = -\frac{1}{2}\)

The answer is:   \(\displaystyle -\frac{1}{2}\)

Reorder the numbers in the data set from least to greatest.

\(\displaystyle [-9,11,-3,1,0]\rightarrow [-9,-3,0,1,11]\)

The median is the central number for an odd set of numbers.

The answer is:  \(\displaystyle 0\)

Reorder the numbers from least to greatest.

\(\displaystyle [2,8,3,0,-5,-4]\rightarrow [ -5,-4,0,2,3,8]\)

For an even number of values in a set of data, the median is the average of the central two numbers.

\(\displaystyle \frac{0+2}{2} = 1\)

The answer is:  \(\displaystyle 1\)

There are thirteen test scores, an odd number, so the median of the test scores is the score which, after the scores are ordered, appears in the middle. Order the scores from greatest to least:

12, 19, 19, 20, 22, 22, 22, 23, 28, 28, 29, 34, 35 

As there are \(\displaystyle N= 13\) scores, we are seeking out the score that ranks at number

\(\displaystyle \frac{N + 1}{2} = \frac{13+1}{2} = 7\) 

That is, the median is the seventh-highest score. This score can be seen to be 22.

There are fourteen test scores, an even number, so the median of the test scores is the arithmetic mean of the two scores which, after the scores are ordered, appear in the middle. Order the scores from greatest to least:

12, 19, 19, 20, 22, 22, 22, 23, 28, 28, 29, 34, 35, 50

As there are \(\displaystyle N= 14\) scores, we are seeking out the score that ranks at number

\(\displaystyle \frac{N }{2} = \frac{14}{2} = 7\)

from the top, and number 7 from the bottom.  

That is, the median is the arithmetic mean of the seventh-highest and seventh-lowest scores. These scores can be seen to be 22 and 23, so the median of the scores is 

\(\displaystyle M = \frac{22+ 23}{2} = \frac{45}{2} = 22.5\)

Reorder the numbers from least to greatest.

\(\displaystyle [-2,-2,-9,-9,10,10]\rightarrow [ -9,-9,-2,-2,10,10]\)

For an even amount of numbers given, the median is the average of the central two numbers.

\(\displaystyle \frac{-2+(-2)}{2} = \frac{-4}{2}\)

The answer is:  \(\displaystyle -2\)

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set.

So, given the data set

\(\displaystyle 88, 81, 90, 94, 85, 95, 90\)

we will arrange the numbers in ascending order (from smallest to largest). We get

\(\displaystyle 81, 85, 88, 90, 90, 94, 95\)

Now, we will find the number in the center. We get

\(\displaystyle 81, 85, 88,{\color{Red} 90}, 90, 94, 95\)

We can see that it is 90.

Therefore, the median of the data set is 90.

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set.

So, given the data set

\(\displaystyle 6, 5, 6, 8, 6, 3, 2, 5, 6, 1, 3\)

we will first arrange the numbers in ascending order (from smallest to largest). So, we get

\(\displaystyle 1, 2, 3, 3, 5, 5, 6, 6, 6, 6, 8\)

Now, we will find the number in the middle.

\(\displaystyle 1, 2, 3, 3, 5, {\color{Red} 5}, 6, 6, 6, 6, 8\)

We can see that it is 5.

Therefore, the median of the data set is 5.