- #1
bigplanet401
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Homework Statement
Player A has a higher batting average than player B for the first half of the baseball season. Player A also has a higher batting average than player B for the second half of the season. Prove, or disprove, that player A has a higher batting average than player B for the entire season.
Homework Equations
Arithmetic mean
The Attempt at a Solution
Let rA, rB be the batting average of A and B, respectively in the first half of the season (and rA', rB' in the second half of the season). I tried to compare the overall average by taking a weighted average of each player's performance in the first and second half (nA and nB are the number of balls hit in the first season, primes for the second season)
[/B]
[tex]
\frac{n_A r_A + n^\prime_A r^\prime_A}{n_A + n^\prime_A} \lessgtr
\frac{n_B r_B + n^\prime_B r^\prime_B}{n_B + n^\prime_B}
[/tex]
But then I get lost when I try to find something that has rA and rB on one side of the inequality sign. The algebra seems to get very tedious and I'm wondering if I'm on the right track.