By that same link, the bottom 10% of the population have less average income than your cost of living.
But I read a little bit more, and it looks like that they are indeed tackling the income inequality problem [1]. Which is where country size and GDP per capita comes into play: a richer country has more money to implement inequality-reducing measures, and implementing them for a 5M people country is far easier than for bigger countries.
> The better society is the one where everyone has an opportunity to improve their lot in life by satisfying a need of others.
Well, that's why inequality is important as a metric. If you're born in a poor household, statistically you'll have far less opportunities than if you're born in a better situation. Want everybody to have an opportunity to improve and succeed? Fight poverty.
1: https://www.straitstimes.com/politics/parliament-inequality-...
Upon independence, "Singapore faced a small domestic market, and high levels of unemployment and poverty. 70 percent of Singapore's households lived in badly overcrowded conditions, and a third of its people squatted in slums on the city fringes. Unemployment averaged 14 percent, GDP per capita was US$516, and half of the population was illiterate." [https://en.wikipedia.org/wiki/Economy_of_Singapore#Independe...]
Compared to today, Singapore has about 1000 homeless, 3.16 persons per household, a literacy rate of 97.3%, GDP per capita of $602 billion, an unemployment rate of 4.11% and a median household income of $9,293. The income distribution isn't bad either. From what I could find the cost of living (minus rent) for an individual is $575 a month.
https://blog.seedly.sg/average-singaporean-household-income-...
The better society is the one where everyone has an opportunity to improve their lot in life by satisfying a need of others.