Where to find data for infographics?

No, Yes, Definitely not.
There is no standard way of collecting data, this is because there are different types of data you can collect and it all does depend on the relevancy to the niche you are doing the infographic on.
Yes you do research for the industry leaders or top niche sites for guidance on the types of data you want need . It also depends on what you wish to say in the infographic.

There are dangers in utilising the last option using data in other people's infographics, you have no idea where they got the data from was it a reputable source government think tank , a University, newspaper survey, or even worse did they make it up. Now I'm sure you don't want to be using something that another web owner has made up with no facts to back it. If you do find infographics or websites that provide stats have a look at the citations, they must have a sentence or a paragraph explaining where they got them. You know wikipedia at the bottom of the pages they have citations a good starting point to follow through on, for your niche.

You want to find news, gov, authority sites with the latest info measured in figures, statistics and results of surveys that sort of thing. Sometimes the world's marketing agencies, SEO associations,Medical, Scientific organizations, Political global, World Health Organisation, even manufacturers (becareful of their angle though) will commission surveys coming up with useful facts and statistics that you might be able to use.

This is a great page to start your search:

United Nations List of National Statistics Offices

Points to the statistics pages of every country in the UN. That should give you some fuel for infographics..

Here's a really helpful webpage about gathering data and statistics with lots of links:
How To Find Statistics and Data | University Libraries

I'm not sure if it is legal to take website data and turn it into information graphic. The owners of these data spent money to gather this data so it is not ethical to get it( or maybe not I'm not a lawyer)

The last message you want to receive is a "Cease and Desist Notice". If you really want to be safe. You can start your own survey or use a public statistics. or better message the owner if it's fine to use their data.

What is your niche? If I knew, I wouldn't mind finding some authoritative (government/university) links for you where you can get statistical data on your subject.

Yeah, I don't think statistical data can be copyrighted.

Here's what the U.S. Census Bureau says:

Copyright protection is not available for any work of the United States Government (Title 17 U.S.C., Section 105). Thus you are free to reproduce census materials as you see fit. We would ask, however, that you cite the Census Bureau as the source.