Topic 4 of 7 · Form 4
Index numbers, weighted averages and vital statistics
Price relative = (price in current year ÷ price in base year) × 100.
Notes for this topic 1 file, in order
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Index numbers
Price relative = (price in current year ÷ price in base year) × 100.
Worked example: A loaf cost US$0.80 in the base year and US$1.00 now. Find the price relative.
1.00 ÷ 0.80 × 100 = 125
Weighted index numbers and weighted averages
Weighted index = Σ(index × weight) ÷ Σweights. Chain base index numbers compare each year with the previous year.
Worked example: Indices 110, 120 and 105 have weights 3, 2 and 5. Find the weighted index.
(330 + 240 + 525) ÷ 10 = 109.5
Crude rates
Crude death (or birth) rate = number of deaths ÷ total population × 1 000.
Worked example: A town of 20 000 people recorded 180 deaths. Find the crude death rate.
180 ÷ 20 000 × 1 000 = 9.0 per thousand
Standardised rates
Remove the effect of different age structures by applying local age-specific rates to a standard population.
Worked example: Age-specific death rates per 1 000: 0–39: 2; 40–59: 8; 60+: 40. Standard population: 60%, 25%, 15%. Find the standardised death rate.
(2 × 60 + 8 × 25 + 40 × 15) ÷ 100 = (120 + 200 + 600) ÷ 100 = 9.2 per thousand
Check yourself
- What does an index of 95 mean?
- Why might a retirement town have a high crude death rate?
- Find the weighted mean of 60 (weight 2) and 80 (weight 3).
Show answers
- Prices are 5% lower than in the base year.
- It has a high proportion of elderly people.
- (120 + 240) ÷ 5 = 72
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