To complete the table, let's determine the missing midpoints and relative frequencies based on the given data.
1. Determine the Midpoints:
The midpoint of a class interval can be found by taking the average of the lower and upper boundaries of the class interval. Using the given class intervals, we calculate the midpoints as follows:
- For the class interval [tex]\( 25-29 \)[/tex]:
[tex]\[
\text{Midpoint} = \frac{25 + 29}{2} = 27
\][/tex]
- For the class interval [tex]\( 30-34 \)[/tex]:
[tex]\[
\text{Midpoint} = \frac{30 + 34}{2} = 32
\][/tex]
2. Determine the Relative Frequencies:
The relative frequency for each class interval can be calculated by dividing the frequency of the class by the total frequency and then multiplying by 100 to convert it to a percentage. Given the total frequency is [tex]\( 8 + 14 + 13 = 35 \)[/tex]:
- For the class interval [tex]\( 25-29 \)[/tex]:
[tex]\[
\text{Relative Frequency} = \left( \frac{14}{35} \right) \times 100 = 40.00\%
\][/tex]
- For the class interval [tex]\( 30-34 \)[/tex]:
[tex]\[
\text{Relative Frequency} = \left( \frac{13}{35} \right) \times 100 = 37.14\%
\][/tex]
Now fill in the table with the obtained values:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
Class interval & Frequency & Midpoint & \begin{tabular}{c}
Relative \\
frequency (\%)
\end{tabular} \\
\hline
20-24 & 8 & 22 & 22.86 \\
\hline
25-29 & 14 & 27 & 40.00 \\
\hline
30-34 & 13 & 32 & 37.14 \\
\hline
\end{tabular}
\][/tex]
Thus, the finalized table should look like this:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
Class interval & Frequency & Midpoint & \begin{tabular}{c}
Relative \\
frequency (\%)
\end{tabular} \\
\hline
20-24 & 8 & 22 & 22.86 \\
\hline
25-29 & 14 & 27 & 40.00 \\
\hline
30-34 & 13 & 32 & 37.14 \\
\hline
\end{tabular}
\][/tex]
