Baseball Statistics.

[mmm4444bot]

Hello everybody:

Here is another precalculus problem that has me stumped.

Player A has a higher batting average than Player B for the first half of the season.

Player A also has a higher batting average than Player B for the second half of the season.

Is it necessarily true that Player A's batting average for the entire season is greater than Player B's?

Batting Average (as I understand it) is number of hits divided by number of at bats.

I wrote a proof (which is flawed) showing that the answer is: Yes. The text's author says the answer is: No.

Will somebody please provide me with a counterexample?

Thank you.

~ Mark

:shock:

 

[tkhunny]

The secret may be in the number of "at bats". If you keep them even, you may have a problem with the premise. What if "A" is injured right after the All-Start Break?

First Half

A: 3/10 = 0.300 -- A is better in the first half.
B: 2/10 = 0.200

Second Half

A: 1/1 = 1.000 -- A is better in the second half.
B: 40/100 = 0.400

Total Season

A: 4/11 = 0.364
B: 42/110 = 0.382 -- B is better for the season.