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Index numbers

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• Converts the information in a time series of numerical information (data).

• Converts each piece of information to represent its value relative to a chosen base.

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Steps in computing index numbers

1. Select a base time period.

2. For each time period, a) divide the value for that time period by the

value for the base period

b) multiply by 100

c) round to a whole number.

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Time # of major crimes

Major crime index

1 16

2 20

3 18

4 24

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Time # of major crimes

Major crime index

1 16

2 (base year) 20 20/20*100

3 18

4 24

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Time # of major crimes

Major crime index

1 16

2 (base year) 20 100

3 18

4 24

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Time # of major crimes

Major crime index

1 16 16/20*100

2 (base year) 20 100

3 18

4 24

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Time # of major crimes

Major crime index

1 16 75

2 (base year) 20 100

3 18

4 24

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Time # of major crimes

Major crime index

1 16 75

2 (base year) 20 100

3 18 18/20*100

4 24

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Time # of major crimes

Major crime index

1 16 75

2 (base year) 20 100

3 18 90

4 24

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Time # of major crimes

Major crime index

1 16 75

2 (base year) 20 100

3 18 90

4 24 24/20*100

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Time # of major crimes

Major crime index

1 16 75

2 (base year) 20 100

3 18 90

4 24 125

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Index numbers

are read as

“percentages of”

the base year.

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Time # of major crimes

Major crime index

1 16 75

2 (base year) 20 100

3 18 90

4 24 125

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Index numbers can be recomputed for a new base:

Divide the index number by the index number of the new base

and multiply by 100.

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Time Major crime index

Re-based index

1 75 75/125*100

2 (base period) 100 100/125*100

3 90 90/125*100

4 (new base) 125 125/125*100

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Time Major crime index

Re-based index

1 75 60

2 (base period) 100 80

3 90 72

4 (new base) 125 100

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Index numbers are computed

to allow easier comparison

of rates of change

of multiple times series.

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Index numbers also are useful for graphing multiple

time series dataof hugely different scales of values.

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Demonstration:CO2 emissions

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