# Mathematics Mode Median and mean Averages

Modes, medians, and means are very different forms of obtaining statistical information about a set of data. When we use the term ‘average’ all scientists and mathematicians think of mean because that is the only true average that can be used for scientific calculations; mode and medians are strongly statistics based. To further compare these types of averages lets define each of these individual things by looking at a particular set.

Example Set :
3,5,7,2,9,9,1,8,8,9,4

Mode (Most Frequent Value):
A mode is the value of a set that is most frequent or appears the most times within a particular set. In our example the mode is 9 because 9 appears three times while 8 only appears twice and every other number only appears once. Since 9 appears the more frequent then every other individual number 9 is the mode of our set.

Median (Middle Value):
A median is the value of a set that is in the middle of the set; and by middle we mean it is greater than half of the set and less than the other half. To find the median will need to order the numbers in order of least to greatest; or vice versa. Here is our reorganized set:1,2,3,4,5,7,8,8,9,9,9. Now we can choose between two different methods to find our median…

Method One is to cross out the least number (1) than the greatest (9) than the next least (2) and the next greatest (9) until you only have one or two numbers left. In this set we only have one remaining number which is 7.

Method Two is to count the total amount of numbers within our set (11) then add 1 and divide it by 2 which will conveniently place us in the middle of our set which is the 6th number which is 7.

Both of these methods work easily because we have an odd amount of numbers (11) in our set. If the total amount of numbers is even we would take the mean between both numbers in the middle. For example if we placed the number 10 at the end of our set using Method One the middle numbers would be 7 & 8; and Method Two would tell us to look at the ((12+1)/2) number or the 6.5th number which would be we would have to look at the 6th and 7th numbers which again are 7 & 8. To find out how to take the mean of these values please refer to the section below.

Mean (Average Value):
A mean is the value of a set in which is the algebraic average. To do this we will take the sum of every number in the set and divide that total by the amount of numbers in the set. So to find the mean of this set we must sum together 3+5+7+2+9+9+1+8+8+9+4=65. Then since we have 11 numbers in our set the mean is 65/11=5.91.

In conclusion, we can see that each of these ‘averages’ are completely different. This is fine because we know that each of these ‘averages’ represent a different aspect of our set. Now that we know how to derive each of these values we can further understand what the significance of these values is and what they can be used for.