What are 'Averages'? By Key Stage Two.com

This information, brought to you by Key Stage Two.com looks at the different types of averages.

The three most common types of averages are Mean, Median, and Mode, and it is important to know what type your values relate to, as the figures can vary greatly depending on the type of average. 

You may also come across the term ‘range’, this is simply the difference between the largest and smallest values.

There are many "averages" in statistics, but Mean, Median, and Mode are the most common that you are likely to encounter in everyday life.  

The "mean" is the "average" that you are probably used to, where you add up all the numbers and then divide by the number of numbers.  I.e. finding the mean of

40, 60, 40, 100, 150, 30, 200, 80.  You add these values together = 700

Then divide by 8, as there are 8 values in the sum= 700 ÷ 8 = 87.5

Therefore the ‘mean’ of this sum is 87.5

The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first.

Taking the same sum as above  40, 60, 40, 100, 150, 30, 200, 80 We will firstly arrange them in order starting with the smallest              30, 40, 40, 60, 80, 100, 150, 200                                 As we have an even number of values, which is eight values we do not have a clear middle value and will have to calculate it manually, therefore the two middle values are 60 and 80, simply add them together 60 + 80 = 140, then divide by 2 = 70.

Therefore the "median" of this sum is 70.     

The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

Remember, it is possible to have more than one mode if there is more than one value which appears the most.

Taking the same sum as above 40, 60, 40, 100, 150, 30, 200, 80.  The value that occurs most often in the sum is 40, as it appears twice and the other values only appear once.

Therefore the "mode" of this sum is 40.

The "range" is just the difference between the largest and smallest values. The range is found by subtracting the lowest value from the highest value.

Taking the same sum as above 40, 60, 40, 100, 150, 30, 200, 80 – The smallest value is 30 and the largest value is 200, so 200 – 30 is 170.

Therefore the “range” of this sum is 170.

Summary

Mean: regular meaning of "average"
Median: middle value
Mode: most often

Range: Difference between the highest and lowest values.

You can see from the above equations the different types of averages can vary depending how you calculate them, make sure you know what type of average your sum is based on to get a clear picture of the values.

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