Question

find the slugging average of a player with the following statistics to the nearest thousandth: hits = 109 d=50 t=2, hr=24, ab=518.

Explanation:

Step1: Recall slugging average formula

The slugging average (SLG) formula is \( SLG=\frac{1\times \text{singles}+2\times \text{doubles}+3\times \text{triples}+4\times \text{home runs}}{\text{at - bats}(AB)} \). First, we need to find the number of singles. We know that total hits \( H=\text{singles}(S)+\text{doubles}(d)+\text{triples}(t)+\text{home runs}(HR) \). So, \( S = H - d - t - HR \). Given \( H = 109 \), \( d = 50 \), \( t = 2 \), \( HR = 24 \), then \( S=109 - 50 - 2 - 24=33 \).

Step2: Calculate total bases

Total bases \( TB=1\times S + 2\times d+3\times t + 4\times HR \). Substitute the values: \( TB = 1\times33+2\times50 + 3\times2+4\times24 \). Calculate each term: \( 33+100 + 6+96=235 \).

Step3: Calculate slugging average

Using the formula \( SLG=\frac{TB}{AB} \), with \( TB = 235 \) and \( AB = 518 \), we have \( SLG=\frac{235}{518}\approx0.454 \) (rounded to the nearest thousandth).

Answer:

\( 0.454 \)