To determine percentiles using a cumulative frequency graph, also known as an ogive, follow these steps:

1. Identify the Desired Percentile: Locate the desired percentile on the vertical axis of the graph. For example, if you are interested in the 25th percentile, find this value on the vertical axis and draw a horizontal line across the graph.

2. Understanding Percentiles: Percentiles represent the values below which a certain percentage of the data falls. For instance, the 25th percentile, also referred to as the first quartile, is the value below which 25% of the data points are situated.

3. Calculate the Total Data Points: Start by determining the total number of data points, which corresponds to the highest value on the cumulative frequency axis. If there are $100$ data points, then the $25$th percentile corresponds to $25\%$ of $100$, which equals $25$.

4. Locate the Cumulative Frequency: On the vertical (cumulative frequency) axis, find the value $25$. From this point, draw a horizontal line until it intersects with the cumulative frequency curve.

5. Determine the Percentile Value: From the point of intersection, draw a vertical line downwards to the horizontal axis (the axis representing data values). The point where this vertical line meets the horizontal axis indicates the value of the $25$th percentile.

6. Repeat for Other Percentiles: To find additional percentiles, such as the $50$th (the median) or the $75$th (the third quartile), locate $50\%$ or $75\%$ of the total number of data points on the cumulative frequency axis and follow the same procedure.

Using a cumulative frequency graph in this manner provides a visual representation that simplifies the interpretation of percentiles, helping to enhance your understanding of the data distribution.