Demographics (Civ5)

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The demographics screen is one of your most important tools for assessing how well you are doing. In single-player games, for each category your rank is displayed in the left-most column, while the average, maximum, and minimum values are to the right. 

Here is a breakdown of the information it gives you and how it is calculated:

Demographic What it represents
Population Relative to the number of 20xPopulation5 Citizens and cities you have. Formula unknown.

The release of the gameCoreDLL shows the "realPopulation" formula in (CvCity.c), that is

long CvCity::getRealPopulation() const
    return (((long)(pow((double)getPopulation(), 2.8))) * 1000);

That is, each city's "real" population is (getPopulation() ^ 2.8) * 1000. So, the population is the sum of each city's "real population."

Crop yield The total 20xFood5 Food produced in all of your cities. This is not your surplus food.
Manufactured goods The total 20xProduction5 Production in all of your cities.

GNP (Gross national product)

The total 20xGold5 Gold collected in all of your cities before expenses.
Land 10,000 times the number of tiles within your borders.

Relative to your military might. The exact formula is unknown but it is influenced by your units, their health and their promotions.

(Square root of your military might) * 2000

Approval 60 + (excess 20xHappiness5 Happiness * 3)
Literacy 0% until you research Writing. Percentage of the technology tree that you have completed. All technologies have the same value.
Civilization V [edit]
Gods & KingsBrave New World

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† Only in vanilla Civ5
‡ Only in Gods & Kings and Brave New World