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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

 

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 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

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 11th 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)