Averages
Averages is the way of getting a more accurate final total from a set of numbers. You can remember the different type of averages by using the following short tune:
Hey Diddle diddle, The median's the middle, you add and divide for the mean, the mode is the one you see the most, the range is the difference between, 

Key terms
Bimodal = a sequence with two modes.
Frequency = How often something occurs. Mean = All the numbers in a sequence added, then divided by the total number of numbers in the sequence. Median = the middle number in a set of numbers that are in numerical order. Midpoint = the middle number. Mode = the number that occurs the most in a set of given numbers. Range = the difference between the highest number and the lowest number in a sequence. Sum = all the numbers added together. Trimodal = a sequence with three modes. 
Median 
Mean 
The median is the method by which you take the largest numbers and the smallest numbers and create a general average which is in the middle. You need to put the numbers in order and then it is in the middle. If you have an odd number of numbers its easy. For example if you had the numbers 11 11 12 13 14. the median would be 12. However if you have a set of even numbers its the middle number between the middle numbers, if that makes any sense. For the sequence 11 12 12 13 14 15. The median will be 12.5 as this is the middle number/ midpoint between 12 and 13.

For the mean you need to add all the numbers that you have together and divide by the number you have. For example if you had a set of 10 numbers you would multiply them all together and then divide by ten. For example in the sequence 2 2 3 3 4 5 7 7 9 9 the first thing you would do is add them all together which equals 55. Then you would divide by the total number there is which in this case is 10 which would give you a mean of 5.5.

RangeThe range of a set of data is the difference between the highest number and the lowest number. To work this out you take the smallest number away from the highest number. For example if the highest number was 67 and the lowest number was 34, the range would be 6734 which equals 33.

ModeThe mode is the most commonly seen number in the set of numbers. For example in a set of numbers if the number 11 is seen the most then this would be the mode of the set of numbers. Is there is two numbers that are seen with the same frequency then this is bimodal (two modes) This continues ongoing for example if there are 3 most common numbers this would be trimodal.

Mean of a frequency table
In an exam you will most likely be given the first two columns (Frequency and shoe size). To find the mean you first need to multiply the frequency by the number in the first column. The mean is then the sum of the frequency column divided by the sum of the third column. In the case of the table to the left an example exam question would be " In science, Sam did an experiment to find the mean shoe size of his class. Using an appropriate table, show the result that Sam would find."

To work this out you would draw the table with the first two columns completed. The next step would be to work out the third column by multiplying the frequency by the category. Next find the sum of both columns, then divide the frequency by the end column to find the mean. A quick tip is if your exam answer is in a bit of a muddle circle your answer, as the examiner will have hundreds of other exam questions to mark and so this will make it easier for them. If the first column is a range for example 1020, 2130,3140, then find the mid point ( the middle number in the range) and then multiply that by the frequency.
Related Resources
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Related Topics
Check the Spec'
AQA Mathematics (8300) S4 Statistics section
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Pearson (Edexcel) Statistics 6 GCSE Maths 19
OCR Maths (J560) 12.03a Summary Statistics