To find the mode of the given frequency distribution, we need to identify the class interval that contains the highest frequency. Let’s go through the steps to determine the mode:
1. Identify the class intervals and their frequencies:
- Class intervals (Cl): [tex]\(10-20, 20-30, 30-40, 40-50, 50-60\)[/tex]
- Frequencies (f): [tex]\(15, 30, 45, 12, 18\)[/tex]
2. Locate the class interval with the highest frequency:
By examining the frequencies, we can see:
- The frequency for [tex]\(10-20\)[/tex] is [tex]\(15\)[/tex].
- The frequency for [tex]\(20-30\)[/tex] is [tex]\(30\)[/tex].
- The frequency for [tex]\(30-40\)[/tex] is [tex]\(45\)[/tex].
- The frequency for [tex]\(40-50\)[/tex] is [tex]\(12\)[/tex].
- The frequency for [tex]\(50-60\)[/tex] is [tex]\(18\)[/tex].
The highest frequency observed is [tex]\(45\)[/tex] which corresponds to the class interval [tex]\(30-40\)[/tex].
3. Determine the mode:
The mode of a dataset is the value that appears most frequently. In the context of grouped data, the mode is the class interval with the highest frequency. Thus, the mode for this distribution is [tex]\(30-40\)[/tex].
So, the mode of the given data is the class interval [tex]\( \mathbf{30-40} \)[/tex] with a frequency of [tex]\(45\)[/tex].
