2

I am trying to find the appropriate formula in order to calculate and represent the 'equality' between a set of values. Let me explain with an example:

Imagine 3 people speaking on an a TV Show that lasts 45 minutes: Person 1 -> 30 minutes spoken Person 2 -> 5 minutes spoken Person 3 -> 10 minutes spoken

I want to find a number that expresses how "equal" was this discussion in matters of time spoken per person. The ideal would be to speak 15 minutes each (100% equality) and the worst case scenario would be to speak only one person for 45 minutes (0% equality).

My first thought, is to use the standard deviation. When the standard deviation is 0 we have perfect equality. As the standard deviation gets larger, the equality is reduced.

The problem with standard deviation, is that is not easily readable for a person who is not familiar with statistics. Can you think of a formula that can help me represent the standard deviation (maybe in conjunction with the mean) as a percentage between 0% and 100% ?

gsach
  • 121
  • If you want something that's "easily readable for a person who is not familiar with statistics", just report the maximum and minimum value. "Talks lasted between 5 and 30 minutes." –  Jun 30 '15 at 13:50
  • If you want to keep it between 0% and 100%, ratio the speaking times on the total time. Person 1, 30:45 (67%); person 2, 5:45 (11%); and person 3, 10:45 (22%). – Laars Helenius Jun 30 '15 at 13:50
  • Anyway, I'll leave this here: https://en.wikipedia.org/wiki/Gini_coefficient –  Jun 30 '15 at 14:47
  • @Rahul The Gini coefficient is exactly what I was looking for. Thank you! Can you post that as an answer so as to accept it? – gsach Jul 01 '15 at 11:21

2 Answers2

0

Are you looking for a good way to use the standard deviation to go from 0% to 100% so that a layperson would understand it better, or are you looking for something to use instead of the standard deviation that a layperson would better understand?

In the first case, I would recommend dividing the standard deviation of "Data 1; Data 2; Data 3; ..." by the standard deviation of "0; 0; ...; Total" (your example would give a standard deviation approximately equal to 50.9% of the maximum possible deviation, giving 100% - 50.9% inequality = 49.1% equality)

Simpson17866
  • 522
  • I thought of this practice and tried it. The problem is that it gives always very big numbers (over 95% for pretty inequal data). Any ideas about using an existing distribution? – gsach Jun 30 '15 at 14:23
0

Finally, thanks to @Rahul, found Gini Coefficient which works great for my case.

The Gini coefficient (also known as the Gini index or Gini ratio) (/dʒini/ jee-nee) is a measure of statistical dispersion intended to represent the income distribution of a nation's residents, and is the most commonly used measure of inequality

https://en.wikipedia.org/wiki/Gini_coefficient

gsach
  • 121