Beginners Guide to Mean, Mode and Median
Created | Updated Jan 27, 2003
An average summarises a group of numbers. There are three main types of averages: mean, mode and median. These will be looked at in turn.
Mean
This is the most commonly used average. The mean is calculated by taking the sum of the numbers in a sample and dividing that by sample size. This is the only type of average that takes into account all the numbers in the sample.
Example - Here is a sample of numbers:
1,2,2,2,3,3,4,6
The first thing to do is add the numbers up. In this case, the result is 23 .
All that is left to do is divide this number by the sample size. In this case, we are dividing 23 by 8 and we get the result 2.875 .
Potential Problems - Mean averages have two linked problems:
- If you have a large number of small values with a few very large values in your sample, mean averages get skewed: the mean is nearer to the bigger values even though the small values are more numerous. If you have a few small values and a few large values, the mean average can get skrewed this way too.
- If you have one, or more, outlying values that do not follow the general trend of the numbers in a sample, the mean average can be affected more dramatically than intended.
1,2,2,2,3,3,4,6,100
The sum of these numbers is 123. If we divide this by the sample size - 9, we get 13.6666(recurring) which does not represent the earlier numbers.
Mode
This type of average is the common number in the sample. Where Mean has problems with representativity, mode focuses on the most common numbers and gives less or no attention to less common numbers.
Example - We'll take another sample of numbers here:
1,2,2,2,3,3,4,6
The mode here is 2 as it appears 3 times. Note: If there are two numbers which are equally common in the sample, then you take both as the mode.
Potential Problems - Mode is less useful when you have a lot of values that are close together but have not been rounded to the nearest whole number. This means an inacurate mode of the numbers will be taken. It would be better in this example to round the numbers first before using mode.
Median
This type of average is the middle number in a sample and requires the numbers to be in order.
Example - Here is another sample of numbers:
4,2,2,6,3,3,1,2
To use the median, these numbers need to be in order. So here they are ordered:
1,2,2,2,3,3,4,6
Here the median is 2.5 . It comes out as this because there is a even sample size here. Therefore there is no middle number. To work out the median, you need to take the 2 and the 3 which are the middle numbers and get the mean of them - which is 2.5 .
With an odd sample it is much easier: you just take the middle number as the median.
Potential Problems - One problem with using median is that it requires the numbers to be put in order first. For a large set of numbers, this can be extremely labourous and tiring.
