# Measures of Central Tendency and Dispersion

## Mean

In this video, we are going to look at how to solve for the mean. The mean is found by adding up all of the numbers in a set, and then dividing it by the total amount of numbers.
For example:
With the set {2, 2, 4, 6, 8, 9, 11, 13}, first add up all the numbers, And then divide it by the amount of numbers, 8. So:
$2+2+4+6+8+9+11+13=55$
$55\div8=6.875$

## Median

In this video, we are going to look at how to solve for the median. The median is the middle number, when the numbers are arranged in numerical order.
For example:
With the set {2, 2, 4, 6, 8, 9, 11, 13, 17}, start crossing off numbers from each side, one by one, until you are left with just the middle number. In this set of numbers, 8 is the median.
In cases like {2, 2, 4, 6, 8, 9, 11, 13}, do the same thing by crossing off numbers from each side, one by one, until you are left with the middle number. In this case, however, we are stuck with two numbers in the middle, 6 and 8. Here, the median would be the number in between these two. The way to find that is to solve for the average of the two remaining numbers. So:
$\frac{6+8}{2}=\frac{14}{2}=7$
In this set of numbers, the median is 7.

## Mode

In this video, we are going to look at how to solve for the mode. The mode is the number that appears most often.
For example:
With the set {2, 2, 4, 6, 8, 9, 11, 13}, the mode would be 2 because 2 appears twice while all other numbers appear only once. Remember that the MODE is the number that appears the MOST.

## Range

In this video, we are going to look at how to solve for the range. The range is the largest number minus the smallest number.
For example:
With the set {2, 2, 4, 6, 8, 9, 11, 13}, the range would simply be 11 because 13-2=11. This set of numbers spans 11 integers.

## Calculate the Mean from a Frequency Table

In this video, we are going to look at how to calculate the mean from a frequency table.
For example:
We can translate the table given in the video into a set of numbers. Since 1 student was absent once, we write 1 once. Since 1 student was absent twice, we write 2 once. Since 3 students were absent three times, we write 3 three times. And so on. This gives us a number set of {1, 2, 3, 3, 3, 4, 4, 5, 5, 6}. From here, we can solve for mean as usual. Add up the values, and then divide by the total amount of students. So:
$1+2+3+3+3+4+4+5+5+6=36$
$36\div10=3.6$
The mean in this number set is 3.6.

## Calculate the Median from a Frequency Table

In this video, we are going to look at how to calculate the median from a frequency table.
For example:
We can translate the table given in the video into a set of numbers. Since 1 student was absent once, we write 1 once. Since 1 student was absent twice, we write 2 once. Since 3 students were absent three times, we write 3 three times. And so on. This gives us a number set of {1, 2, 3, 3, 3, 4, 4, 5, 5, 6}. From here, we can solve for median as usual. Cross off numbers from each side, one by one, until you are left with just the middle number. In this set, we are left with 3 and 4 being in the middle. That means that we have to find the average of these two numbers. So:
$\frac{3+4}{2}=3.5$
In this set of numbers, the median is 3.5.

## Calculate the Mode from a Frequency Table

In this video, we are going to look at how to calculate the mode from a frequency table.
For example:
In this table, 3 absences appear 3 times. That is more than any other number of absences in the table. By simply analyzing the table, we can determine that the mode is 3.

## Calculate the Range from a Frequency Table

In this video, we are going to look at how to calculate the range from a frequency table.
For example:
To find the range of absences, just simply subtract the largest number minus the smallest number. Based on this table, we can clearly see that the largest number of absences is 6 and the smallest number of absences is 1. Therefore, 6-1=5. The range is 5.