The frequency table below represents the 30 best batting averages for a semi-pro baseball league. Which ranges of batting averages were least common among the players?

\begin{tabular}{|c|c|}
\hline Batting Average & Frequency \\
\hline [tex]$0.320-0.329$[/tex] & 1 \\
\hline [tex]$0.330-0.339$[/tex] & 2 \\
\hline [tex]$0.340-0.349$[/tex] & 12 \\
\hline [tex]$0.350-0.359$[/tex] & 14 \\
\hline [tex]$0.360-0.369$[/tex] & 1 \\
\hline
\end{tabular}

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]



Answer :

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.