To construct a frequency table with a class interval of width 5 starting at -0.5, we will follow these steps:
1. Define the Class Intervals:
The class intervals will be:
[tex]\[
(-0.5, 4.5), (4.5, 9.5), (9.5, 14.5), (14.5, 19.5), (19.5, 24.5), (24.5, 29.5), (29.5, 34.5), (34.5, 39.5), (39.5, 44.5)
\][/tex]
2. Tally the Frequencies:
We will count how many data points fall within each class interval.
3. Calculate the Relative Frequencies:
Relative frequency is calculated by dividing the frequency of each class interval by the total number of data points (which is 100).
Based on the given data, let's construct the frequency table:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Class Interval} & \text{Frequency} & \text{Relative Frequency} \\
\hline
-0.5 - 4.5 & 12 & 0.12 \\
4.5 - 9.5 & 42 & 0.42 \\
9.5 - 14.5 & 24 & 0.24 \\
14.5 - 19.5 & 13 & 0.13 \\
19.5 - 24.5 & 5 & 0.05 \\
24.5 - 29.5 & 1 & 0.01 \\
29.5 - 34.5 & 2 & 0.02 \\
34.5 - 39.5 & 0 & 0.00 \\
39.5 - 44.5 & 1 & 0.01 \\
\hline
\end{array}
\][/tex]
Let’s summarize the results in a more structured table:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\text{Class Interval} & \text{Frequency} & \text{Relative Frequency} \\
\hline
-0.5 - 4.5 & 12 & 0.12 \\
4.5 - 9.5 & 42 & 0.42 \\
9.5 - 14.5 & 24 & 0.24 \\
14.5 - 19.5 & 13 & 0.13 \\
19.5 - 24.5 & 5 & 0.05 \\
24.5 - 29.5 & 1 & 0.01 \\
29.5 - 34.5 & 2 & 0.02 \\
34.5 - 39.5 & 0 & 0.00 \\
39.5 - 44.5 & 1 & 0.01 \\
\hline
\end{tabular}
\][/tex]
This table shows the frequency and relative frequency of the price-earnings ratios of the 100 common stocks in the specified class intervals.
