Let's break down how we determine the frequency and relative frequency distributions step by step.
Given the frequency data:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Class Limits} & \text{Frequency (f)} \\
\hline
21-25 & 4 \\
26-30 & 3 \\
31-35 & 12 \\
36-40 & 10 \\
41-45 & 6 \\
46-50 & 8 \\
\hline
\end{tabular}
\][/tex]
To find the relative frequency for each class, we use the formula:
[tex]\[
\text{Relative Frequency} = \left( \frac{f}{n} \right) \times 100
\][/tex]
where [tex]\( n \)[/tex] is the total number of students, which is 48 in this case.
1. For the class interval 21-25:
[tex]\[
\text{Relative Frequency} = \left( \frac{4}{48} \right) \times 100 = 8 \%
\][/tex]
2. For the class interval 26-30:
[tex]\[
\text{Relative Frequency} = \left( \frac{3}{48} \right) \times 100 = 6 \%
\][/tex]
3. For the class interval 31-35:
[tex]\[
\text{Relative Frequency} = \left( \frac{12}{48} \right) \times 100 = 25 \%
\][/tex]
4. For the class interval 36-40:
[tex]\[
\text{Relative Frequency} = \left( \frac{10}{48} \right) \times 100 = 21 \%
\][/tex]
5. For the class interval 41-45:
[tex]\[
\text{Relative Frequency} = \left( \frac{6}{48} \right) \times 100 = 12 \%
\][/tex]
6. For the class interval 46-50:
[tex]\[
\text{Relative Frequency} = \left( \frac{8}{48} \right) \times 100 = 17 \%
\][/tex]
So, the frequency and relative frequency distributions are as follows:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\text{Class Limits} & \text{Frequency (f)} & \text{Relative Frequency} \\
\hline
21-25 & 4 & 8 \% \\
26-30 & 3 & 6 \% \\
31-35 & 12 & 25 \% \\
36-40 & 10 & 21 \% \\
41-45 & 6 & 12 \% \\
46-50 & 8 & 17 \% \\
\hline
\end{tabular}
\][/tex]
This completes the frequency and relative frequency distributions for the given data.
