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Worked Examples · Example 15

Q.In a country, the life expectancy at birth is 70 years. If the UNDP's goalposts for life expectancy are a minimum of 20 years and a maximum of 85 years, calculate the life expectancy dimension index used in computing the HDI.

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Formula:

Dimension Index=Actual value−Minimum valueMaximum value−Minimum value\text{Dimension Index} = \dfrac{\text{Actual value} - \text{Minimum value}}{\text{Maximum value} - \text{Minimum value}}

Given: Actual life expectancy = 70 years; Minimum goalpost = 20 years; Maximum goalpost = 85 years.

Solve (first pass):

Index=70−2085−20=5065=0.7692\text{Index} = \dfrac{70 - 20}{85 - 20} = \dfrac{50}{65} = 0.7692

Independent verification (second pass): Recompute the denominator and numerator separately — numerator 70−20=5070-20=50; denominator 85−20=6585-20=65; 50/65=0.76923...50/65 = 0.76923..., rounding to 0.7690.769. Both passes match, confirming the result. …

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