Teach GCSE Maths Index Numbers Index Farmland Birds Woodland Birds U.K. Bird Populations Year

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Many things increase in price from one year to another. The following table shows the prices of a toy and a game in 2000 and We can easily see that the price of the toy has increased more than that of the game Price of toy ( £ ) 1020 Price of game ( £ ) Increase Price of toy ( £ ) Price of game ( £ ) Toy Game Year Price ( £ )

Now let’s compare the prices of the same toy with a different game. The toy has increased by the same amount as the 2 nd game... or has it ? Price of toy ( £ ) 1020 Price of 2 nd game ( £ ) Increase Price of toy ( £ ) Price of 2 nd game ( £ ) There are different ways of comparing price increases. Toy 2 nd Game Year Price ( £ )

Increase Price of toy ( £ ) 10 Price of 2 nd game ( £ ) 10 Let’s work out the 2005 prices as a percentage of the prices in  100 = Toy: 20  100 = Game: 200% 150% The price of the toy has increased by 100% since 2000 but the game is only 50% more than its price in We have based this calculation on taking the 2000 prices as 100%. If we drop the % sign we have an index

Year Price ( £ ) Index Price ( £ ) Index Toy Game We now have the following graphs: Toy 2 nd Game Price ( £ ) Year Price ( £ ) Toy 2 nd Game Index Numbers Year Index

e.g.The graph shows the price index for the average cost of a house bought by a first time buyer. Source: Office for National Statistics, Social Trends 37 Year Price Index (a)When was the price twice its 1995 value? In 1995, the index was 100 and the cost was thousand. £46·5 (b) The index was 304 in What was the cost?

e.g.The graph shows the price index for the average cost of a house bought by a first time buyer. Source: Office for National Statistics, Social Trends 37 Year Price Index (a)When was the price twice its 1995 value? Solution: For twice the price we need 200%. £46·5 The price had doubled during In 1995, the index was 100 and the cost was thousand.

e.g.The graph shows the price index for the average cost of a house bought by a first time buyer. Year Price Index Solution: so, in 2005 the cost was  46· = £141·36 thousand 304 £46·5 (b) The index was 304 in What was the cost? In 1995 the cost was £46·5 In 1995, the index was 100 and the cost was thousand.

We can use index numbers to compare changes in quantities other than money. The next graph shows indexes for the UK populations of woodland and farmland wild birds.

e.g. Source: Office for National Statistics, Social Trends 34. Year Index Farmland Birds Woodland Birds U.K. Bird Populations (a)Which year is the base year? (b)Do we know how many birds there were in the base year? Ans: 1970 Ans: No. Index numbers never give actual values.

e.g. (c)The index for the farmland birds was (i) 116 in 1977, and (ii) 64 in What do you think these numbers mean? Ans:(i)In 1977 there were 16% more farmland birds than in Year Index Farmland Birds Woodland Birds U.K. Bird Populations (ii)In 1998 the population had dropped to 64% of the 1970 value x x

 Percentage changes are obvious from the index values. SUMMARY  An index number is used to compare changes in quantities over time.  The index for the quantities being compared is usually set to 100 in the base year.  The base year is always at the start of the period so all the quantities start at the same point. e.g. If the index is 100 in the base year, Increase of 20% from base year Index 120: Decrease to 70% of base year value. Index 70:

Exercise 1.The number of acts of vandalism had increased by 125% by Vandalism Vehicle Thefts Crime in England and Wales Source: Office for National Statistics, Social Trends 37 For each statement below choose one of the following: (a) true (b) false (c) we can’t tell There were 1·8 million vehicle thefts in There were more vehicle thefts than acts of vandalism throughout most of the period shown. 3.There were about 4·4 million vehicle thefts in 1995.

Exercise 1. The number of acts of vandalism had increased by 125% by Vandalism Vehicle Thefts Crime in England and Wales Source: Office for National Statistics, Social Trends 37 Ans: False The number had increased to 125% of the 1981 value. This is an increase of 25%. Solution:

Exercise Vandalism Vehicle Thefts Crime in England and Wales Source: Office for National Statistics, Social Trends There were more vehicle thefts than acts of vandalism throughout most of the period shown. Ans: We can’t tell We are given no information about the number of acts of vandalism, only the changes in the number. Solution:

Exercise Vandalism Vehicle Thefts Crime in England and Wales Source: Office for National Statistics, Social Trends There were about 4·4 million vehicle thefts in Ans: True We were told there were 1·8 million in By 1995, the index has increased to about ·  = 4·4 million Solution: