Understanding the Frequency Distribution
The given data represents a frequency distribution across multiple class intervals. This is a fundamental concept in statistics, particularly useful for summarizing large datasets.

Class Intervals and Frequencies
- Class intervals: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-100
- Corresponding frequencies: 8, 7, 12, 23, 11, 13, 8, 6, 12

Interpreting the Data
- **Frequency**: Indicates how many observations fall within each interval.
- **Distribution Shape**: Analyzing frequencies can help identify the distribution shape (e.g., normal distribution, skewness).

Calculating Additional Statistics
- **Total Frequency**: Sum of all frequencies = 8 + 7 + 12 + 23 + 11 + 13 + 8 + 6 + 12 = 100.
- **Mode**: The interval with the highest frequency (40-50) indicates the mode, which is the most common range.

Graphical Representation
- **Histogram**: A visual representation can be created using a histogram to show the frequency distribution. Each interval will be represented by a bar, with heights corresponding to their frequencies.
- **Ogive**: A cumulative frequency graph can also be plotted for better understanding of cumulative distributions.

Conclusion
This frequency table is valuable for summarizing, analyzing, and visualizing data. It aids in understanding patterns and trends, essential for making informed decisions or further statistical analysis in exams such as UPSC.