the difference between batting .250 and .300

I read the following in a book recently, and I'm still not sure I believe it.

If you watch baseball enough, you know that there is a world of difference between a batter with an average of .250 and one who bats .300. The former will probably have to justify being in the everyday lineup with qualities other than batting: his defense, or perhaps an otherwise high total of runs batted in. And the latter just might make the All-Star team with a .300 batting average! 

Now check the math here and see if it's correct: in 20 at-bats, getting five hits would yield an average of .250, and yet just one hit more out of 20 would produce an average of .300. 

Five hits in 20 at-bats vs. six hits in 20 at-bats. And that could be the difference between being a starter... or riding the bench.