Talk:Gini coefficient#Gini in Template:infobox country

It seems to me the current formula in the article might be slightly incorrect. Here is the current formula:

:$G\; =\; \backslash frac\{\backslash displaystyle\{\backslash sum\_\{i=1\}^n\; \backslash sum\_\{j=1\}^n\; \backslash left|\; x\_i\; -\; x\_j\; \backslash right|\}\}\{\backslash displaystyle\{2\; \backslash sum\_\{i=1\}^n\; \backslash sum\_\{j=1\}^n\; x\_j\}\}\; =\; \backslash frac\{\backslash displaystyle\{\backslash sum\_\{i=1\}^n\; \backslash sum\_\{j=1\}^n\; \backslash left|\; x\_i\; -\; x\_j\; \backslash right|\}\}\{\backslash displaystyle\{2n\backslash sum\_\{j=1\}^n\; x\_j\}\}\; =\; \backslash frac\{\backslash displaystyle\{\backslash sum\_\{i=1\}^n\; \backslash sum\_\{j=1\}^n\; \backslash left|\; x\_i\; -\; x\_j\; \backslash right|\}\}\{\backslash displaystyle\{2\; n^2\; \backslash bar\{x\}\}\}$

Specifically, the current numerator suggests it would include each person's difference from themself, i.e., $x\_i-x\_j$, where $i=j$. However, if $j$ is defined as the set of all other persons who aren't $i$, then the upper limit of $j$'s index ought to be $n-1$. Thus, I believe the numerator ought to be:

::$\backslash displaystyle\{\backslash sum\_\{i=1\}^n\; \backslash sum\_\{j=1\}^\{n-1\}\; \backslash left|\; x\_i\; -\; x\_j\; \backslash right|\}$

Moreover, I propose that the article be updated to explicitly define $j$.

Lastly, I'm not sure whether the denominator needs any updating. MosesRivera100 (talk) 19:07, 7 September 2023 (UTC)

:These formulas added later may be wrong. Take $x\_1\; =\; 1;\; \backslash ;\backslash ;\backslash ;\; x\_2\; =\; 0$

:Using these would give: $G\; =\; \backslash frac\{1\}\{2n^2\}\; \backslash frac\{\backslash sum\_i\; \backslash sum\_j\; |x\_i\; -\; x\_j|\}\{\backslash bar\{x\}\}\; =\; \backslash frac\{1\}\{8\}\; \backslash times\; \backslash frac$

1 - 0| + |0-1

{0.5} = \frac{1}{2}

:Now use $G\; =\; \backslash frac\{\backslash text\{mean\; absolute\; difference\}\}\{\backslash text\{mean\}\}\; =\; \backslash frac\{\backslash bar\{\backslash Delta\}\}\{\backslash bar\{x\}\}$

:Where $\backslash bar\{\backslash Delta\}\; =\; \backslash frac\{1\}\{n\}\; \backslash sum\_i\; \backslash sum\_\{j\; >\; i\}\; |x\_i\; -\; x\_j|\; =\; \backslash frac\{1\}\{2n\}\; \backslash sum\_i\; \backslash sum\_j\; |x\_i\; -\; x\_j|$

:and $\backslash bar\{x\}\; =\; \backslash frac\{1\}\{n\}\; \backslash sum\_i\; x\_i$

:You'll get the correct value of 1. In this case, $G\; =\; \backslash frac\{\backslash sum\_i\; \backslash sum\_j\; |x\_i\; -\; x\_j|\}\{2\; \backslash sum\_i\; x\_i\}$ 2804:1998:421:F201:88E7:6514:10BF:CCDF (talk) 19:57, 25 June 2024 (UTC)

Mathworld's article on the Gini Coefficient:

https://mathworld.wolfram.com/GiniCoefficient.html

Am I missing something? This wiki article makes it seem like the Gini coefficient is difficult to use and fraught with pitfalls without giving many concrete definitions, while the Mathworld reference has two easy-to-understand formulas. What's up with that? 24.228.174.225 (talk) 21:51, 5 August 2024 (UTC)

Gini Coefficient only measures income inequality and not wealth inequality and text(s) saying that should be removed.

The source [2] for the statement that

"Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality" doesn't even say or imply that.

Wealth inequality is always greater than income inequality, and Gini only measures income inequality. It is very misleading to say/imply that wealth inequality is at the same level as income inequality. Egalitaristen (talk) 20:15, 4 March 2025 (UTC)