To find the mode of the given grouped data, we need to determine the class interval that has the highest frequency. Here is a step-by-step process:
1. List the class intervals with their corresponding frequencies:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Class Interval} & \text{Frequency} \\
\hline
20-30 & 5 \\
\hline
30-40 & 3 \\
\hline
40-50 & 12 \\
\hline
50-60 & 2 \\
\hline
60-70 & 6 \\
\hline
70-80 & 2 \\
\hline
\end{array}
\][/tex]
2. Identify the class interval with the highest frequency:
- The frequencies are: 5, 3, 12, 2, 6, 2.
- The highest frequency is 12.
3. Determine the modal class:
- The class interval corresponding to the highest frequency (which is 12) is 40-50.
Thus, the mode of the given data is the interval (40, 50), and the frequency of this modal class is 12. Therefore, the mode of the data is:
[tex]\[
\text{Modal class} = [40-50]
\][/tex]
[tex]\[
\text{Frequency of the modal class} = 12
\][/tex]
