How do you find the mode using a cumulative frequency graph?

To find the mode using a cumulative frequency graph, identify the steepest part of the curve.

In more detail, the mode is the value that appears most frequently in a data set. When using a cumulative frequency graph, also known as an ogive, the mode corresponds to the point where the graph has the steepest gradient. This is because the steepest part of the curve indicates the interval with the highest frequency of data points.

To locate this on the graph, first, plot the cumulative frequency against the data values. The cumulative frequency is the running total of frequencies up to each data point. As you plot these points and connect them with a smooth curve, observe where the curve rises most sharply. This steep section represents the interval where the data values are most concentrated, indicating the mode.

For example, if you have a cumulative frequency graph for the ages of students in a school, and the curve rises most sharply between the ages of 14 and 15, this interval likely contains the mode. To be more precise, you can look at the original frequency table to pinpoint the exact age within that interval.

Remember, the cumulative frequency graph is a useful tool for visualising data distribution, and identifying the steepest part of the curve can help you quickly estimate the mode.