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To construct the frequency table for the given price-earnings (P/E) ratios of 100 common stocks using a class interval width of 5 starting at -0.5, we need to determine the range of the data and the corresponding class intervals.
Class Intervals:
Given the class interval width of 5 starting at -0.5, the class intervals would be:
- Class Interval 1: [tex]\([-0.5, 4.5)\)[/tex]
- Class Interval 2: [tex]\([4.5, 9.5)\)[/tex]
- Class Interval 3: [tex]\([9.5, 14.5)\)[/tex]
- Class Interval 4: [tex]\([14.5, 19.5)\)[/tex]
- Class Interval 5: [tex]\([19.5, 24.5)\)[/tex]
- Class Interval 6: [tex]\([24.5, 29.5)\)[/tex]
- Class Interval 7: [tex]\([29.5, 34.5)\)[/tex]
Frequency Table:
We will now fill in the frequency of P/E ratios within each class interval.
Frequency Count:
- For class interval [tex]\([-0.5, 4.5)\)[/tex], we have 12 stocks with P/E ratios (values: 1, 3, 1, 3, 1, 3, 1, 1, 3, 1, 1, 3).
- For class interval [tex]\([4.5, 9.5)\)[/tex], we have 42 stocks with P/E ratios (values: 5, 7, 7, 7, 7, 7, 7, 5, 7, 8, 5, 5, 7, 8, 8, 5, 8, 5, 7, 8, 5, 8, 8, 5, 8, 7, 8, 8, 7, 5, 8, 5, 7, 8, 5, 8, 7, 5, 8, 8, 5, 7).
- For class interval [tex]\([9.5, 14.5)\)[/tex], we have 25 stocks with P/E ratios (values: 10, 12, 14, 10, 13, 10, 12, 14, 14, 10, 12, 14, 11, 14, 10, 14, 13, 14, 11, 12, 12, 14, 11, 12, 11).
- For class interval [tex]\([14.5, 19.5)\)[/tex], we have 13 stocks with P/E ratios (values: 15, 15, 18, 16, 17, 16, 18, 19, 16, 15, 16, 19, 19).
- For class interval [tex]\([19.5, 24.5)\)[/tex], we have 5 stocks with P/E ratios (values: 21, 24, 24, 24, 21).
- For class interval [tex]\([24.5, 29.5)\)[/tex], we have 1 stock with P/E ratio (value: 26).
- For class interval [tex]\([29.5, 34.5)\)[/tex], we have 2 stocks with P/E ratios (values: 31, 34).
Now, we can tabulate these intervals and their corresponding frequencies:
[tex]\[ \begin{tabular}{|l|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline -0.5 - 4.5 & 12 \\ 4.5 - 9.5 & 42 \\ 9.5 - 14.5 & 25 \\ 14.5 - 19.5 & 13 \\ 19.5 - 24.5 & 5 \\ 24.5 - 29.5 & 1 \\ 29.5 - 34.5 & 2 \\ \hline \end{tabular} \][/tex]
Thus, the frequency table is:
\begin{tabular}{|l|c|}
\hline
\text{Class Interval} & \text{Frequency} \\
\hline
-0.5 - 4.5 & 12 \\
4.5 - 9.5 & 42 \\
9.5 - 14.5 & 25 \\
14.5 - 19.5 & 13 \\
19.5 - 24.5 & 5 \\
24.5 - 29.5 & 1 \\
29.5 - 34.5 & 2 \\
\hline
\end{tabular}
This table displays the number of common stocks within each price-earnings ratio class interval.
Class Intervals:
Given the class interval width of 5 starting at -0.5, the class intervals would be:
- Class Interval 1: [tex]\([-0.5, 4.5)\)[/tex]
- Class Interval 2: [tex]\([4.5, 9.5)\)[/tex]
- Class Interval 3: [tex]\([9.5, 14.5)\)[/tex]
- Class Interval 4: [tex]\([14.5, 19.5)\)[/tex]
- Class Interval 5: [tex]\([19.5, 24.5)\)[/tex]
- Class Interval 6: [tex]\([24.5, 29.5)\)[/tex]
- Class Interval 7: [tex]\([29.5, 34.5)\)[/tex]
Frequency Table:
We will now fill in the frequency of P/E ratios within each class interval.
Frequency Count:
- For class interval [tex]\([-0.5, 4.5)\)[/tex], we have 12 stocks with P/E ratios (values: 1, 3, 1, 3, 1, 3, 1, 1, 3, 1, 1, 3).
- For class interval [tex]\([4.5, 9.5)\)[/tex], we have 42 stocks with P/E ratios (values: 5, 7, 7, 7, 7, 7, 7, 5, 7, 8, 5, 5, 7, 8, 8, 5, 8, 5, 7, 8, 5, 8, 8, 5, 8, 7, 8, 8, 7, 5, 8, 5, 7, 8, 5, 8, 7, 5, 8, 8, 5, 7).
- For class interval [tex]\([9.5, 14.5)\)[/tex], we have 25 stocks with P/E ratios (values: 10, 12, 14, 10, 13, 10, 12, 14, 14, 10, 12, 14, 11, 14, 10, 14, 13, 14, 11, 12, 12, 14, 11, 12, 11).
- For class interval [tex]\([14.5, 19.5)\)[/tex], we have 13 stocks with P/E ratios (values: 15, 15, 18, 16, 17, 16, 18, 19, 16, 15, 16, 19, 19).
- For class interval [tex]\([19.5, 24.5)\)[/tex], we have 5 stocks with P/E ratios (values: 21, 24, 24, 24, 21).
- For class interval [tex]\([24.5, 29.5)\)[/tex], we have 1 stock with P/E ratio (value: 26).
- For class interval [tex]\([29.5, 34.5)\)[/tex], we have 2 stocks with P/E ratios (values: 31, 34).
Now, we can tabulate these intervals and their corresponding frequencies:
[tex]\[ \begin{tabular}{|l|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline -0.5 - 4.5 & 12 \\ 4.5 - 9.5 & 42 \\ 9.5 - 14.5 & 25 \\ 14.5 - 19.5 & 13 \\ 19.5 - 24.5 & 5 \\ 24.5 - 29.5 & 1 \\ 29.5 - 34.5 & 2 \\ \hline \end{tabular} \][/tex]
Thus, the frequency table is:
\begin{tabular}{|l|c|}
\hline
\text{Class Interval} & \text{Frequency} \\
\hline
-0.5 - 4.5 & 12 \\
4.5 - 9.5 & 42 \\
9.5 - 14.5 & 25 \\
14.5 - 19.5 & 13 \\
19.5 - 24.5 & 5 \\
24.5 - 29.5 & 1 \\
29.5 - 34.5 & 2 \\
\hline
\end{tabular}
This table displays the number of common stocks within each price-earnings ratio class interval.
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