SME
Human Geography
Political geography and development
Use this for “A country has life expectancy 75 years, mean schooling 10 years, expected schooling 15 years and GNI $20,000 a person. Find its HDI.”
Chart
This is an example. Type your own values to start a new problem.
LE
Life expectancy
example · years
MYS
Mean schooling
example · years
EYS
Expected schooling
example · years
GNI
GNI per person
example · $
IH
Health index
calculated
IE
Education index
calculated
II
Income index
calculated
HDI
Human Development Index
calculated
tier
Development tier
worked out (not typed)
Formulas
IH
=
LE − 20
65
0.8462
=
75 − 20
65
IE = (MYS ÷ 15 + min(EYS ÷ 18, 1)) ÷ 2
0.75
=
10 ÷ 15 + min(15 ÷ 18, 1)
2
II
=
ln
min(GNI ÷ 100, 750)
ln(750)
0.8003
=
ln
min(20,000 ÷ 100, 750)
ln(750)
HDI = ∛(IH × IE × II)
0.7979 = ∛(0.8462 × 0.75 × 0.8003)
tier = low if HDI < 0.55, medium if HDI < 0.7, high if HDI < 0.8, else very high
0.7979 < 0.8, so high
Assumptions
•
The goalposts are the UNDP’s: life expectancy 20 to 85 years, schooling 15 years (mean) and 18 years (expected), income $100 to $75,000.
•
Each index places the country between its goalposts, from 0 to 1 (a value past a goalpost counts as the goalpost); income counts by its log, since each extra dollar adds less.
•
The HDI is the geometric mean of the three indices, so one low index can’t be hidden by high ones.
•
UNDP tiers: low under 0.550, medium under 0.700, high under 0.800 and very high from 0.800.
Step-by-step
WE KNOW
LE = 75 years, MYS = 10 years, EYS = 15 years, GNI = $20,000
FIND
health index (IH), education index (IE), income index (II), Human Development Index (HDI), development tier (tier)
Step 1 · Find health index (IH)
Use IH = (LE − 20) ÷ 65
Count the years past the 20-year floor, out of the 65 years between the goalposts.
IH
=
75 − 20
65
IH
=
55
65
IH = 0.8462
Step 2 · Find education index (IE)
Use IE = (MYS ÷ 15 + min(EYS ÷ 18, 1)) ÷ 2
Each kind of schooling is measured against its own top (expected schooling counts at most 18 years), then the two shares are averaged.
IE
=
10 ÷ 15 + min(15 ÷ 18, 1)
2
10
15
=
0.6667
15
18
=
0.8333
0.6667 + 0.8333
2
=
0.75
IE = 0.75
Step 3 · Find income index (II)
Use II = ln(min(GNI ÷ 100, 750)) ÷ ln(750)
Income counts by its log: how many times the $100 floor it is (at most the 750 times of the $75,000 top), against those 750 times.
II
=
ln
min(20,000 ÷ 100, 750)
ln(750)
20,000
100
=
200
ln(200) = 5.298
ln(750) = 6.62
5.298
6.62
=
0.8003
II = 0.8003
Step 4 · Find Human Development Index (HDI)
Use HDI = ∛(IH × IE × II)
The geometric mean: multiply the three indices, then take the cube root.
HDI = ∛(0.8462 × 0.75 × 0.8003)
0.8462 × 0.75 × 0.8003 = 0.5079
∛0.5079 = 0.7979
HDI = 0.7979
Step 5 · Find development tier (tier)
Use tier = low if HDI < 0.55, medium if HDI < 0.7, high if HDI < 0.8, else very high
The UNDP sorts countries into four tiers by their HDI, cut at 0.55, 0.7 and 0.8.
0.7979 < 0.8: high
tier = the UNDP tier that holds HDI
tier = the UNDP tier that holds 0.7979
tier = high
Check
Put the numbers back in. Both sides should match.
0.8462
=
75 − 20
65
✓
0.75
=
10 ÷ 15 + min(15 ÷ 18, 1)
2
✓
0.8003
=
ln
min(20,000 ÷ 100, 750)
ln(750)
✓
0.7979 = ∛(0.8462 × 0.75 × 0.8003) ✓
0.7979 < 0.8, so high ✓
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