RAY: Hi! We're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to talk about cars, car repair, and the answer to last week's Puzzler. And this one was from the Baseball Algebraic Series.
TOM: There aren't many of those.
RAY: No.
TOM: No. The only one.
RAY: This is a stand-alone.
TOM: A series of one.
RAY: Here it is. There are two rookie players, and we call them Bluto and Popeye. On opening day, they made a wager on who would have the best batting average at the end of the season. So here it is. It's the last game of the season, and nothing's going to change because neither of these guys is in the starting lineup. So Bluto says, "Hey, Popeye. What did you bat for the first half of the season?" Popeye says, "I am what I am and it's all that I am, and I batted .250." Bluto says, "I got you there. I batted .300." Then Bluto asks, "How about after the All-Star break?" And Popeye proudly pipes up, "I batted .375." Bluto says, "Pretty good. You know what I batted? .400."
TOM: Mmmm.
RAY: Fork over that 20 bucks that we bet.
TOM: And I believe you also said that they had the same number of at-bats.
RAY: I did. It was then that Dougie the batboy saunters over and says, "Don't pay the 20 bucks. I think you won."
TOM: Huh?
RAY: How could that be?
TOM: Mmm.
RAY: And how many times did he hit him with the bat? Well, here it is.
TOM: Go ahead, man. I can hardly wait.
RAY: Let's assume that they both had 600 at-bats.
TOM: Is that a lot?
RAY: That's about average for a guy who plays the whole season except for the last game.
TOM: OK. He had 600 at-bats.
RAY: OK?
TOM: Yeah.
RAY: If Bluto batted .300 for the first half of the season...
TOM: Mmm-hmm.
RAY: And he had 500 at-bats during that first half of the seasonÉ
TOM: Oooh. Yeah.
RAY: He got 150 hits. One hundred fifty over 500 is .300 average, right?
TOM: Mmm-hmm. So he would have gotten 150.
RAY: Yeah. OK? If Popeye batted .250 and had 100 at-bats, he would have had 25 for 100.
TOM: Mmm-hmm.
RAY: OK? You with me so far?
TOM: I'm with you.
RAY: The second half of the season, Bluto bats .400. How does he do that? Well, we know he had 500 at-bats in the first half.
TOM: So he's only been up 100 times in the second half of the season.
RAY: And he got 40 hits.
TOM: And he got 40 hits. Got it.
RAY: Popeye bats .375.
TOM: But he's up 500 times.
RAY: And he gets 187 and a half hits. One of them was a chuck-swing single over the infield. They only count that as half a hit.
TOM: Yeah.
RAY: So now, let's...let's figure it all out.
TOM: So we got...
RAY: Bluto batted 600 times. How many total hits did he get?
TOM: 190, I have.
RAY: Right. How about Popeye? How many hits did he get?
TOM: 212.
RAY: 212 and a half.
TOM: And a half.
RAY: And when you figure that out, Bluto batted .316 for the season.
TOM: Yeah.
RAY: Right? Even though he batted .300 and .400 in each half.
TOM: Yeah.
RAY: And Popeye bats .353 and wins the batting title.
TOM: No kidding!
RAY: Pretty good, huh?
TOM: Pretty darned good. A good little example of the arithmetic mean and what it means to me.
RAY: And how statistics can lie, more importantly.
TOM: Wow! That's good. Now, you know that every fifth-grade teacher in the country will be using this problem next week.
RAY: I hope so.
TOM: I hope so.
RAY: Because it's a good one.
TOM: And what they should do is take bets. Teach the kids about betting.
RAY: Right!
TOM: And they should give odds, teach the kid about odds. That's good.
RAY: They can cover all the bases, so to speak.
TOM: Cover all the bases, so to speak.
RAY: So, who's our winner?
TOM: The winner is Mike Bennett from Dallas, Texas. And, for having his answer selected at random from among all the correct answers, Mike is going to get a $25 gift certificate to the store at the Car Talk section of cars.com.[ Car Talk Puzzler ]
