Editing Human Development Index (section)

=== Old method (HDI before 2010) ===
The HDI combined three dimensions last used in its 2009 report:

* [[Life expectancy]] at birth, as an index of population health and longevity to HDI 
* Knowledge and education, as measured by the adult [[literacy]] rate (with two-thirds weighting) and the combined primary, secondary, and tertiary [[gross enrollment ratio]] (with one-third weighting).
* [[Standard of living]], as indicated by the [[natural logarithm]] of [[gross domestic product]] [[per capita]] at [[purchasing power parity]].

[[File:Human Development Index trends.svg|thumb|right|upright=1.25|HDI trends between 1975 and 2004

{| style="width:100%;"
|-
| valign=top |
{{legend|black|[[OECD]]}}
{{legend|#FF0000|[[Europe]] (not in the OECD), and [[Commonwealth of Independent States|CIS]]}}
{{legend|#E45600|[[Latin America]] and the [[Caribbean]]}}
{{legend|#D09B00|[[East Asia]]}}
| valign=top |
{{legend|#00FF00|[[Arab League]]}}
{{legend|#003FD9|[[South Asia]]}}
{{legend|#C600FF|[[Sub-Saharan Africa]]}}
|}
]]

This methodology was used by the UNDP until their 2011 report.

The formula defining the HDI is promulgated by the United Nations Development Programme ([[UNDP]]).<ref>{{Cite web|url=http://hdr.undp.org/en/statistics/faq/question,68,en.html|archive-url=https://web.archive.org/web/20071220162154/http://hdr.undp.org/en/statistics/faq/question%2C68%2Cen.html|url-status=dead|title=Definition, Calculator, etc. at UNDP site|archive-date=20 December 2007|access-date=26 May 2020}}</ref> In general, to transform a raw [[Variable (mathematics)|variable]], say <math>x</math>, into a unit-free [[Index (economics)|index]] between 0 and 1 (which allows different indices to be added together), the following [[formula]] is used:

* <math>x\text{ index} = \frac{x - a}{b - a}</math>

where <math>a</math> and <math>b</math> are the [[maxima and minima|lowest and highest values]] the variable <math>x</math> can attain, respectively.

The Human Development Index (HDI) then represents the uniformly weighted sum with {{frac|1|3}} contributed by each of the following factor indices:

* [[Life Expectancy Index]] <math> = \frac{\text{LE} - 25} {85-25} = \frac{\text{LE} - 25} {60}</math>
* [[Education Index]] <math> = \frac{2} {3} \times \text{ALI} + \frac{1} {3} \times \text{GEI} </math>
** [[Adult Literacy Index]] (ALI) <math> = \frac{\text{ALR} - 0} {100 - 0} = \frac{\text{ALR}} {100}</math>
** [[Gross Enrollment Index]] (GEI) <math> = \frac{\text{CGER} - 0} {100 - 0} =\frac{\text{CGER}} {100}</math>
* [[GDP]] <math> = \frac{\log(\text{GDPpc}) - \log(100)} {\log(40000) - \log(100)} = \frac{\log(\text{GDPpc}) - \log(100)} {\log(400)}</math>
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