Cumulative Frequency Distribution:
A cumulative frequency distribution is a statistical technique used to organize and summarize data. It involves grouping data into intervals and recording the number of occurrences within each interval. In addition to the frequency of each interval, a cumulative frequency column is added, which represents the running total of frequencies as the intervals progress.

Ogive:
An ogive, also known as a cumulative frequency curve, is a graphical representation of a cumulative frequency distribution. It is constructed by plotting the cumulative frequency against the upper boundary of each interval. The resulting curve provides a visual representation of the cumulative frequencies and allows for the identification of patterns and trends in the data.

Characteristics of an Ogive:
An ogive graph possesses the following characteristics:

1. Smooth Curve: The ogive is typically represented by a smooth curve that connects the plotted points.

2. Starting Point: The ogive starts from the cumulative frequency of the first interval, which is usually zero.

3. Ending Point: The ogive ends at the cumulative frequency of the last interval, which represents the total number of data points.

4. Increasing or Decreasing: The ogive can be increasing or decreasing depending on the distribution of the data. If the cumulative frequency increases as the intervals progress, the ogive will be increasing. Conversely, if the cumulative frequency decreases, the ogive will be decreasing.

Advantages of an Ogive:
The ogive offers several advantages in data analysis:

1. Visualization: The ogive provides a visual representation of the cumulative frequency distribution, making it easier to interpret and understand the data.

2. Trend Analysis: By observing the shape and slope of the ogive, trends and patterns in the data can be identified. For example, a steep slope indicates a rapid increase in cumulative frequency, while a flatter slope suggests a slower increase.

3. Percentiles and Quartiles: The ogive can be used to determine percentiles and quartiles. By locating specific points on the ogive, corresponding values can be identified, allowing for the calculation of percentiles and quartiles.

Conclusion:
In summary, the graphical representation of a cumulative frequency distribution is called an ogive. It is a smooth curve that plots the cumulative frequency against the upper boundary of each interval. The ogive offers visualization of the data, trend analysis, and the ability to determine percentiles and quartiles.