1. We will look at
Simple Index Numbers
Chain base index numbers
Weighted index numbers
Retail Price index

2. Simple Index Numbers
These are used to see how the price of things vary over time.
There is always a starting year from which you consider the change in prices. This is called the base year.
The base year has the index number 100.
The simple index number tells you the percentage change since the base year.
Examples
If the base year was 2002 (index number 100) and the simple index number for 2005 is 107 then there has been a rise of 7% between 2002 and 2005.
If the simple index number for 2008 is 94 then there has been a drop of 6% between 2002 and 2008.
Formulae
Simple index number = current price base year x 100

3. Example
The table gives information about the mean price, to the nearest £1000, of terraced houses in the north-west in March 2005 and March 2008.
taking 2005 as the base year, work out the index number for the mean price of terraced houses in the north-west in Give your answer to the nearest whole number
Using as the base year, the index number of the mean price of terraced houses for March 2009 was 110.
By what percentage has the mean price of terraced houses change between 2005 and 2009?
Work out the mean price of terraced houses in 2009
Describe in words what has happened to house prices over the years between 2005 and 2009
Year
2005
2008
Price (£)
80 000
95 000
Index number = 𝟗𝟓𝟎𝟎𝟎 𝟖𝟎𝟎𝟎𝟎 x 100 = index number = 119 to nearest whole number
10%
Mean price is (10% of ) = £ £8 000 = £88 000
The prices increased between 2005 and 2008 but dropped between 2008 and 2009

4. Chain base Index Numbers
These are used to see how the price each year compares with the previous year.
Formulae
Chain base index number = current price previous years price x 100
Example
The table shows the price of a camera over 4 years
The chain base index numbers for 2008 and 2009 are:
For x 100 = for x 100 = 90
The price between 2007 and 2008 went up by 14.3%
The price between 2008 and 2009 went down by 100 – 90 = 10%
Year
2006
2007
2008
2009
Price (£)
£150
£175
£200
£180

5. Weighted Index Numbers
These are a way of comparing weighted means
Formulae
Weighted index number = current weighted mean price base year weighted mean price x 100
Example
The weighted mean for the cost of a bag of groceries in 2009 was 140p
The weighted mean for the same bag of groceries in 2007 was 125p.
The weighted index number for the price of this bag of groceries in taking 2007 as the base year is
x 100 = 112
Price has gone up 12%

6. Retail Price index
This is a weighted index number that shows how the price of a basket of groceries changes from year to year.
It is commonly used for updating old age pensions
It is also used for wage bargaining
The index includes the following categories
Food and catering
Alcohol and tobacco
Housing and household expenditure
Personal expenditure
Travel and leisure
Page 157 for a nice pie chart

7. Your turn
Exercise 4K page 158