Median

The median is the middle value of the set in increasing order.

In this set of 8 (or any even number) entries, the median is the mean of the two middle entries of the set in increasing order

or

To find the median, first you arrange the numbers in order from least to greatest.

Then you count how many numbers you have and divide that number by two. In this case 12,15,16,21,22,32,93,108= 8 numbers.

So

Then starting from the least side of the numbers count 4 numbers till you reach the median number of

Then starting from the greatest side count 4 numbers until you reach the other median number of

Finally find the mean of the two numbers by adding them together and dividing them by two

to find the median number of .

The mean is just the average of all the test scores, which is found by adding up the scores and dividing by the number of scores (). This gives as the mean. The mode is the score which occurs most frequently. In this case, the mode is . The median, the middle score of the sequence, is .

Reorder the numbers in ascending order (from lowest to highest):

11, 13, 13, 13, 13, 14, 16, 19

Find the middle number. In this case, the middle number is the average of the 4th and 5th numbers. Because both the 4th and 5th number are 13, the answer is simply 13.

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.

Rearrange the data set from least to greatest.

Since this data set is even, the median the average of the central two numbers.

The answer is:

To find the median of a set of values, simply place the numbers in order and find the value that is exactly "in the middle." Here, we can place the test scores in ascending order to get , , , , . (Descending order would work just as well.) The median is the middle value, . Make sure you don't confuse median with mean (average)! To get the mean value of this set, you would find the sum of the test scores and then divide by the number of values.

The set is already in increasing order. We have six numbers in the set and we need to ensure the set will have a median of . When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. The two middle numbers represent and . Let's set up an equation.

.

The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by , and subtract on both sides, we get to be . Finally, to find , we need a number that is greater than or equal to and less than or equal to . Answer , satisfies all conditions.

To find the median, find the number that is in the middle of the set when all of the numbers are ordered from smallest to largest.

First order the numbers in the set from smallest to largest:

In this case, our answer and the middle number of the set is:

First regroup all numbers in chronological order.

Since there is an even amount of numbers in the dataset, 6 numbers total, the median will be the average of the third and fourth numbers.

Find the mean of the two numbers.