How many a) Small b) Mid-sized and c) Large Companies are there in the
US?  What is the definition used for the above segments?  What is your
source for this data?

When people talk about small, medium, and large companies, they almost
invariably  define those categories in terms of number of employees.
Unfortunately, there are no hard and fast rules for defining the
number of employees for each category.

For example, I can show you articles on the web in which "large" is
defined as 500 or more employees:
://www.google.com/search?client=googlet&q=large%20%22500%20employees%22

But I can also show you some articles in which "large" is defined as
1,000 or more employees:
://www.google.com/search?hl=en&lr=&client=googlet&q=large+%221,000+employees%22&btnG=Google+Search

Similarly, there are no fixed rules for "small" and "medium," but 100
employees  seems to be very common dividing line between the two:
://www.google.com/search?client=googlet&q=small%20%22100%20employees%22

Basically, if you want to follow the most common approach, the
categories are:

Small: 1-99 employees
Medium: 100-499 employees
Large: 500 or more employees

For the number of companies that fall into each category, the most
convenient place to go is the U.S. Census Bureau [
http://www.census.gov/csd/susb/susb.htm ] Specifically, this Census
Bureau breaks down firm size by the number of employees for 1999 (the
most recent year available):
http://www.census.gov/epcd/susb/1999/us/US--.HTM

You'll notice that the Census Bureau's breakdown is even more narrow
(e.g. 10-19 employees), so it'll be necessary to combine some
categories if you want small/medium/large. This is just for
illustration, and you'll probably want to do your own computation, but
here are my calculations:

Small (1-99 employees): 4,800,582
Medium (100-499 employees): 81,347
Large (500 or more employees): 16,740

I hope this helps. Good luck in your research.

Good logic.  Good Source.  Well thought out.  Reasonable Editoral response as well.

Of course there are many other ways to measure the "size" of a company.
The most common, besides employees is -
a) Market cap = small cap, mid-cap, and large capitalization companies.
This is what Wall Street uses.
b) Revenues - another measure of size.

Also consider percent growth, stock price, P/E ratio, etc.

Vince