Organize the data set from least to greatest.

\(\displaystyle [-3,9,-5,0,-33,-77,23]\rightarrow[-77,-33,-5,-3,0,9,23]\)

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

The answer is:  \(\displaystyle -3\)

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.

\(\displaystyle [-9,30,5,-7] \rightarrow [ -9,-7,5,30]\)

Average the two center numbers in the data set.

\(\displaystyle \frac{-7+5}{2} = \frac{-2}{2}=-1\)

The answer is:  \(\displaystyle -1\)

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

\(\displaystyle [ -6,33,-8,50] \rightarrow [-8,-6,33,50]\)

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.

\(\displaystyle \frac{-6+33}{2} = \frac{27}{2}\)

The answer is:  \(\displaystyle \frac{27}{2}\)

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.

\(\displaystyle \frac{66+84}{2} = 75\)

The answer is:  \(\displaystyle 75\)

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.

\(\displaystyle [-9,3,-9,18,-9,8] \rightarrow [ -9,-9,-9,3,8,18]\)

Average the center two numbers.

\(\displaystyle \frac{-9+3}{2} = \frac{-6}{2}\)

The answer is:  \(\displaystyle -3\)

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.

\(\displaystyle \frac{-8+13}{2} = \frac{5}{2}\)

The median is:  \(\displaystyle \frac{5}{2}\)

Reorganize all the numbers from least to greatest.

\(\displaystyle [-5,11,-9,-15]\rightarrow [-15,-9,-5,11]\)

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

Average the two numbers.

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

The median is:  \(\displaystyle -7\)

Step 1:

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

 \(\displaystyle 2768, 2772, 2787, 2801, 2805, 2877\)

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.

 \(\displaystyle (2787+2801) / 2\)

\(\displaystyle 2794\) 

Solution: \(\displaystyle 2794\)

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

Arrange the data in numerical order.

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

Therefore, the median is 21.

The correct answer is \(\displaystyle 43\). 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. 

\(\displaystyle 12, 20, 20, 23, 42, 43, 50, 59, 59, 83, 95\)

From here, find the middle value. In this case, that is the \(\displaystyle 6\)^th value, \(\displaystyle 43\).