What is the method to find the median using a cumulative frequency graph?

To find the median using a cumulative frequency graph, locate the 50th percentile on the cumulative frequency axis.

A cumulative frequency graph, also known as an ogive, is a useful tool for visualising the distribution of data. To find the median, you first need to determine the total number of data points, which is the highest value on the cumulative frequency axis. The median is the value that separates the data into two equal halves, so you need to find the point that corresponds to half of the total frequency.

For example, if the total frequency is 100, you would look for the 50th percentile, which is 50. Draw a horizontal line from the 50 on the cumulative frequency axis until it intersects the ogive. From this intersection point, draw a vertical line down to the horizontal axis (the x-axis). The point where this vertical line meets the x-axis is the median of your data set.

This method works because the cumulative frequency graph shows the running total of frequencies up to each data point. By finding the 50th percentile, you are effectively identifying the middle value of the data set, which is the definition of the median. This graphical method is particularly useful for large data sets where calculating the median manually would be cumbersome.