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
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
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)