Final answer:
The correct graph to represent cumulative frequencies for numerical data is an ogive. This graph type displays cumulative frequency against class boundaries and is connected by a line or freehand curve. Histograms, frequency polygons, and time series graphs are used for different types of data presentation.
Step-by-step explanation:
The graph to represent the cumulative frequencies for the numerical data will be an ogive. An ogive is a graph that represents the cumulative frequencies for each class boundary plotted at the right end of the class intervals. The points are then connected by a line, typically a freehand curve. The ogive is useful for determining the number of observations below a particular value in a dataset.
Other types of graphs like histograms, frequency polygons, and time series graphs serve different purposes. A histogram is used for displaying large, continuous, quantitative datasets using bars of equal width where the height represents the frequency. Frequency polygons are a type of line graph used for large datasets, making data points that repeat easy to interpret. Time series graphs display data over a period of time, emphasizing the change in one variable.
In contrast, a pie chart represents parts of a whole as slices of a pie, which is not suitable for displaying cumulative frequencies. Therefore, the correct answer is A. ogive.