INDEX NUMBERS FOR TIME SERIES CCEA GCSE Statistics

Index Numbers for Time Series Index numbers measure the relative change in a set of measurements over time, e. g. , the Dow Jones Industrial Average (DJIA), the Consumer Price Index (CPI), the New York Stock Exchange (NYSE) Index CCEA GCSE Statistics requires knowledge of calculating three types of index numbers for time series data: 1. 2. 3. Simple (Base Period) Index Number Chain Base Index Number Weighted Index Number

1) Simple (Base Period) Index Number The Simple Index Number shows how a variable in any given time period has changed relative to a specified base period The formula is given as:

1) Simple (Base Period) Index Number For example, for the data in the table below, calculate the simple price indices for 2015 and 2016 relative to 2014 (the base period) These index numbers show that: prices in 2015 increased by 5% relative to 2014 prices in 2016 increased by 8. 9% relative to 2014

2) Chain Base Index Number The Chain Base Index Number shows how a variable in any given time period has changed relative to the previous time period The formula is given as:

2) Chain Base Index Number For example, considering the data in the previous table, we can calculate the chain base price indices for 2015 and 2016 as follows: These index numbers show that: prices in 2015 increased by 5% relative to 2014 prices in 2016 increased by 3. 7% relative to 2015

3) Weighted Index Number The Weighted Index Number is an index number which is made up from several different index numbers The extent to which each of these index numbers contributes to the overall weighted index number is determined by weightings The formula is given as:

3) Weighted Index Number For example, a factory uses four different chemicals (A, B, C and D) in a manufacturing process. The proportions in which the four chemicals are used are given in the table below Also provided in the table is the 2017 Price Index for each chemical using 2010 as the base year

3) Weighted Index Number We are required to calculate the overall weighted price index of the chemicals in 2017 relative to 2010 To do this we multiply each proportion (w) by the corresponding 2017 Price Index (i) number We then work out the sum of the wi products (Ʃwi) and divide it by the sum of the proportions (Ʃw) as follows: This means that relative to 2010 there has been an 18. 1% overall increase in the cost of the chemicals required for the manufacturing process