ScottRiqui wrote:"Great majority" doesn't have a strict definition, but it might help to remember that "great" is referring to the relative size of the group within the whole, not the actual number itself.
There are 143 million women in the U.S., which is a great number, but it's only a very slight majority (50.9%) compared to the number of men. Likewise, the "great majority" (~98%) of U.S. Presidents have been white males, even though there have only been 43 of them.
1)Great majority of americans like Obama.(40 percent)
2)Slight majority hates him 30 percent
3)30 percent is neutral doesn`t feel anything about him
So in this scenario great majority doesn`t have to be most of the people which includes 50 plus 1.
That`s where u are wrong.
Case 1) from your example isn't a majority, it's a plurality.
Case 2) isn't any kind of a majority at all.
When you're talking about a population 'X':
"None of X" means zero percent.
"Some of X" means a percentage greater than zero (could be as high as 100%, although it's not commonly used that way)
"Majority of X" or "Most of X" means some percentage greater than 50%.
"Great majority", "vast majority", or "overwhelming majority" don't have strict definitions, other than the fact that they are majorities (greater than 50%). Personally, I wouldn't use "great majority" unless the majority was more than 80% of the population, and I would save "vast" and "overwhelming" for cases where the majority is greater than 95% of the population.