Finding averages and comparing distributions for GCSE

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

Height	Frequency
(2.5)	3
(7.5)	2
(15)	6
(30)	1
TOTAL	12

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 6^th and the 7^th 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	1 2 4 6 7	KEY	1	1	= £11
2	1 2 2 2 5 5 7
3	3 4 5 6
4	1 9
5	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 11^th value we find it is £25

Boy’s range:

Comparison:

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)