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Batting Averages

In this topic, you will apply your knowledge of percentages and mean to baseball.
To review mean, see here.

Example 1:

 In 530 at bats, a baseball player has a batting average of 0.241. In the next game, he has 4 at bats. What is the most likely number of hits he will get? Suppose he hits 3 of those swings. What is his new batting average to three places? Most likely number of hits: New batting average:
Part 1: Most likely number of hits
The baseball player has a batting average of 0.241 after 530 at bats. This means that he has a 24.1% chance of getting a hit whenever he swings at a ball.
1. The most likely number of hits is the number of hits × batting average.
So for the next 4 hits, the most likely number of hits is 4 × 0.241 = 0.964

2. We then round to the nearest whole number of hits.
0.964 hits rounds to 1 hit

Part 2: New batting average
 Batting average =
We calculate the new batting average using the fact that after his 530 at bats, the baseball player made 3 more hits from 4 more swings.
 New batting average = =
 Original number of hits = original batting average × original number of swings = 0.241 × 530 = 127.73 which rounds to 128
 New batting average = = = 0.245

Most likely number of hits:
New batting average:

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