To determine which ranges of batting averages were least common among the players, we need to identify the ranges with the lowest frequency values from the given table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Batting Average} & \text{Frequency} \\
\hline
0.320-0.329 & 1 \\
\hline
0.330-0.339 & 2 \\
\hline
0.340-0.349 & 12 \\
\hline
0.350-0.359 & 14 \\
\hline
0.360-0.369 & 1 \\
\hline
\end{array}
\][/tex]
Step-by-Step Solution:
1. Identify the frequencies of each range:
\- [tex]$0.320-0.329$[/tex]: 1 \
\- [tex]$0.330-0.339$[/tex]: 2 \
\- [tex]$0.340-0.349$[/tex]: 12 \
\- [tex]$0.350-0.359$[/tex]: 14 \
\- [tex]$0.360-0.369$[/tex]: 1
2. Find the minimum frequency:
\- By examining the frequencies, we see that the smallest frequency is 1.
3. Identify the ranges associated with this minimum frequency:
\- The two ranges that have a frequency of 1 are [tex]$0.320-0.329$[/tex] and [tex]$0.360-0.369$[/tex].
4. Match these ranges to the answer choices:
\- We need to find the choice that lists both [tex]$0.320-0.329$[/tex] and [tex]$0.360-0.369$[/tex].
5. Analyze the answer choices:
- A. [tex]$0.320-0.329$[/tex] and [tex]$0.330-0.339$[/tex]
- B. [tex]$0.340-0.349$[/tex] and [tex]$0.350-0.359$[/tex]
- C. [tex]$0.330-0.339$[/tex] and [tex]$0.360-0.369$[/tex]
- D. [tex]$0.320-0.329$[/tex] and [tex]$0.360-0.369$[/tex]
6. Select the correct answer:
- The correct answer must be the choice that includes the ranges [tex]$0.320-0.329$[/tex] and [tex]$0.360-0.369$[/tex].
- Thus, the correct answer is:
[tex]\[
\boxed{D}
\][/tex]
So, the ranges [tex]$0.320-0.329$[/tex] and [tex]$0.360-0.369$[/tex] were the least common among the players. The correct answer is D.
