Find the median of the following data set:

To find the median, we should first put our numbers in increasing order:

Next, the median will simply be the number in the middle. 

We have 11 terms, so our median will be the 6th term in the sequence:

So 54 is our median

Find the median of this data set:

To begin, let's put our numbers in increasing order:

Next, find the median by finding the number in the middle of  the data set. If there are two numbers in the middle, then find their average:

So, the median will be:

Find the median of the following data set:

Let's begin by putting our data in increasing order:

Now, the median should be pretty straightforward to find.

The median will simply be the number in the middle of all the terms. 

In this case, it is the number in red below

So our answer is 67.

The key to solving this problem is to first write the numbers in ascending order. 

77, 80, 35, 76, 99, 95, 86, 65, 72, 56, 21

21, 35, 56, 65, 72, 76, 77, 80, 86, 95, 99

After this you will find the middle number of the set which turns out to be .

21, 35, 56, 65, 72, 76, 77, 80, 86, 95, 99

We first plug each of the  values into the function:

Next, we put the answers in order from least to greatest:

Now, to find the median, we find the value that is in the middle of the data set. Since our data set has an odd number of entries the median will be the value that have an equal number of values to either side of it. In this particular case that value lies at the third entry which is 3.

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

Reorder the data set from least to greatest.

Since there are four numbers provided, the median is the average of the second and third numbers.

Average the two numbers.

The median is:  

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

Negative half is less than negative two-fifth.

Since this is an even number set of numbers, the median is the average of the middle two numbers.

Average the two fractions.

Rewrite the complex fraction using a division sign.

Change the division sign to multiplication and take the reciprocal of the second number.

The median is:  

The median of an even number set is the average of the center two numbers in a chronological ordered set from least to greatest.

To arrange the data set, we will need to compare numerators of the similar denominator.

Find the least common denominator.  The least common denominator is  since it is the minimum number divisible by all of the existing denominators.

Convert all fractions to the common denominator.

The data set becomes:  

We can now see that the middle two numbers are:  

Average these two numbers.

The answer is:  

In order to solve for the median, we will need to rearrange the data set in chronological order from least to greatest.

In an even set of data, the median is the average of the central two numbers.

Average the center two numbers.

The median is:  

The numbers not in chronological order.

Change the fractions and the integer to a common denominator.  The common denominator of the fractions is  since this is the least number that is divisible by each of the denominators given.

Convert the fractions.

The median of an even data set is the mean of the center two numbers in a chronological ordered data set from least to greatest.  

The central numbers are  and .

Average these numbers.

The answer is: