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This section explored the many different problems you may be faced with when having to find an average.

It also shows a number of examples of COMPARING distributions.


AVERAGES from Tables

Below is an example of a table of CONTINUOUS data


To estimate the mean:

·       We to find the mid-points of each of the classes which I will write in red

·       We also need to find the total frequency















To estimate the MEDIAN without drawing a cumulative frequency graph

To find which value is the MEDIAN we use the formula


In this case, n=12

The 6th and the 7th value are both in the class: . So our median class is


AVERAGES from STEM and LEAF diagrams


This table shows pocket money of boys in a class



1 2 4 6 7






= £11


1 2 2 2 5 5 7








3 4 5 6








1 9








2 2 3








We already know that the girls have got a mean of £23, a median of £26 and a range of £30.


QUESTION: Compare the amount which boys and girls receive in pocket money.



Boy’s mean: we need to add up each value in the stem and leaf diagram and divide by the number of numbers there are



Boy’s median: we know that n=21


If we count along to find the 11th value we find it is £25


Boy’s range:



1)    The boys’ range is £42 which is £12 more than the girl’s range. This means the amount which boy’s received is more spread out/less consistent.

2)    The boy’s mean of £29.50 is £6.50 more than the girl’s mean. However, the boy’s median of £25 is £1 less. On balance, however, you would suggest that the higher mean indicated that boy’s, on average, receive MORE pocket money


MEDIAN’s and QUARTILES WITHOUT a cumulative frequency graph


Assuming the data is given in ascending order (if not, you need to re-arrange it first)


KEY FORMULA: (where n=the number of data values)

Example: (numbers is red link to the LQ and UQ below)