The median of a given frequency distribution can be found graphically with the help of an ogive. An ogive is a graphical representation of a cumulative frequency distribution. It is constructed by plotting the cumulative frequencies against the upper class boundaries.

Here's how the process works:

1. Create a frequency distribution table: Start by creating a frequency distribution table that includes the class intervals, frequencies, and cumulative frequencies. The cumulative frequency is calculated by adding up the frequencies of all the previous classes.

2. Plot the cumulative frequencies: On a graph paper, plot the upper class boundaries on the x-axis and the cumulative frequencies on the y-axis. Each point represents the cumulative frequency for that particular class.

3. Connect the points: Connect the plotted points with straight lines to form a curve. This curve is called an ogive.

4. Find the median: The median of the frequency distribution can be determined by locating the point on the ogive that corresponds to half of the total frequency. This point represents the median class.

5. Determine the median value: Once the median class is identified, find the lower and upper boundaries of the median class. Subtract the cumulative frequency of the class preceding the median class from the total frequency and divide the result by the frequency of the median class. Multiply this value by the class width and add it to the lower boundary of the median class. The result is the median value.

The ogive allows us to visually identify the median class and calculate the median value by taking into account the cumulative frequencies of the frequency distribution. By connecting the plotted points and analyzing the curve, we can determine the median more accurately and precisely.