Editing Human Development Index (section)

=== New method (2010 HDI onwards) ===
[[File:Human Development Index regions evolution 1990-2021-fr.svg|thumb|right|upright=1.5|HDI trends between 1990 and 2021

{| style="width:100%;"
|-
| valign=top |
{{legend|#7f7f7f|[[List of sovereign states|World]]}}
{{legend|#1f77b4|[[OECD]] countries}}
| valign=top |
Developing countries:
{{legend|#ff7f0e|[[Arab States]]}}
{{legend|#2ca02c|[[East Asia]] and the Pacific}}
{{legend|#d62728|[[Europe]] and [[Central Asia]]}}
{{legend|#9467bd|[[Latin America]] and the [[Caribbean]]}}
{{legend|#8c564b|[[South Asia]]}}
{{legend|#e377c2|[[Sub-Saharan Africa]]}}
|}
]]

Published on 4 November 2010 (and updated on 10 June 2011), the 2010 Human Development Report calculated the HDI combining three dimensions:<ref>{{cite web |title=Human Development Report 2010 |date=4 November 2010 |publisher=UNDP |url=http://hdr.undp.org/en/content/human-development-report-2010 |access-date=15 December 2015 |archive-url=https://web.archive.org/web/20151222145515/http://hdr.undp.org/en/content/human-development-report-2010 |archive-date=22 December 2015 |url-status=live  |last1=Nations |first1=United }}</ref><ref>{{cite web |title=Technical notes |year=2013 |publisher=UNDP |url=http://hdr.undp.org/sites/default/files/hdr_2013_en_technotes.pdf |access-date=15 December 2015 |archive-url=https://web.archive.org/web/20150616130523/http://hdr.undp.org/sites/default/files/hdr_2013_en_technotes.pdf |archive-date=16 June 2015 |url-status=live  }}</ref>

* A long and healthy life: [[Life expectancy at birth]]
* [[Education index|Education]]: Mean years of schooling and expected years of schooling
* A decent standard of living: [[Gross national income|GNI]] per capita ([[Purchasing power parity|PPP]] [[international dollar]]s)
In its 2010 Human Development Report, the UNDP began using a new method of calculating the HDI. The following three indices are used:

1.{{anchor|Life Expectancy Index}} Life Expectancy Index (LEI) <math>= \frac{\textrm{LE} - 20}{85-20} = \frac{\textrm{LE} - 20}{65}</math>
::LEI is equal to 1 when [[life expectancy at birth]] is 85 years, and 0 when life expectancy at birth is 20 years.
2. [[Education Index]] (EI) <math>= \frac{{\textrm{MYSI} + \textrm{EYSI}}} {2}</math><ref>{{Cite news|url=http://www.indiastudychannel.com/resources/141517-New-method-of-calculation-of-Human-Development-Index-HDI.aspx|title=New method of calculation of Human Development Index (HDI)|date=1 June 2011|work=India Study Channel|access-date=19 November 2017|language=en|archive-url=https://web.archive.org/web/20171110171412/http://www.indiastudychannel.com/resources/141517-New-method-of-calculation-of-Human-Development-Index-HDI.aspx|archive-date=10 November 2017|url-status=live}}</ref>
:2.1 Mean Years of Schooling Index (MYSI) <math>= \frac{\textrm{MYS}}{15}</math><ref>Mean years of schooling (of adults) (years) is a calculation of the average number of years of education received by people ages 25 and older in their lifetime based on education attainment levels of the population converted into years of schooling based on theoretical duration of each level of education attended. Source: {{cite journal |last1=Barro |first1=R. J. |author-link=Robert Barro |first2=J.-W. |last2=Lee |year=2010 |title=A New Data Set of Educational Attainment in the World, 1950–2010 |journal=NBER Working Paper No. 15902 |series=Working Paper Series |url=http://www.nber.org/papers/w15902 |doi=10.3386/w15902 |access-date=29 July 2011 |archive-url=https://web.archive.org/web/20110807191234/http://www.nber.org/papers/w15902 |archive-date=7 August 2011 |url-status=live  |doi-access=free }}</ref>
:: Fifteen is the projected maximum of this indicator for 2025.
:2.2 Expected Years of Schooling Index (EYSI) <math>= \frac{\textrm{EYS}}{18}</math><ref>(ESYI is a calculation of the number of years a child is expected to attend school, or university, including the years spent on repetition. It is the sum of the age-specific enrollment ratios for primary, secondary, post-secondary non-tertiary and tertiary education and is calculated assuming the prevailing patterns of age-specific enrollment rates were to stay the same throughout the child's life. Expected years of schooling is capped at 18 years. (Source: UNESCO Institute for Statistics (2010). Correspondence on education indicators. March. Montreal.)</ref>
:: Eighteen is equivalent to achieving a [[master's degree]] in most countries.
3. Income Index (II) <math>= \frac{\ln(\textrm{GNIpc}) - \ln(100)}{\ln(75,000) - \ln(100)} = \frac{\ln(\textrm{GNIpc}) - \ln(100)}{\ln(750)}</math>
::II is 1 when GNI per capita is $75,000 and 0 when GNI per capita is $100.
Finally, the HDI is the [[geometric mean]] of the previous three normalized indices:

: <math>\textrm{HDI} = \sqrt[3]{\textrm{LEI}\cdot \textrm{EI} \cdot \textrm{II}}.</math>

<small>LE: [[Life expectancy at birth]]<br />
MYS: Mean years of schooling (i.e. years that a person aged 25 or older has spent in formal education)<br />
EYS: Expected years of schooling (i.e. total expected years of schooling for children under 18 years of age, incl. young men and women aged 13–17)<br />
GNIpc: [[List of countries by GNI (PPP) per capita|Gross national income at purchasing power parity per capita]]</small>
{{Break}}