A cumulative percentage frequency distribution is a way of organizing and presenting data in a graphical or tabular format. It shows the percentage of observations that fall within a given range of values, and the distribution is cumulative, meaning that the percentage is calculated by adding together the frequencies of all the values that are less than or equal to the upper bound of each range.

To create a cumulative percentage frequency distribution, you first need to organize your data into classes or ranges. These classes should be mutually exclusive, meaning that each value should belong to only one class, and they should also be exhaustive, meaning that all the values in the dataset should be included in at least one class. The classes should also be of equal size, so that you can easily compare the frequencies of different ranges.

Once you have determined the classes, you can calculate the frequencies for each class by counting the number of observations that fall within that range. Then, you can calculate the cumulative percentage frequency for each class by adding together the frequencies of all the classes that are less than or equal to the upper bound of the current class.

For example, let's say you have a dataset of 100 values and you want to create a cumulative percentage frequency distribution with classes ranging from 0-9, 10-19, 20-29, and so on. The first step would be to count the number of values in each class. Let's say you have 10 values in the 0-9 class, 20 values in the 10-19 class, 15 values in the 20-29 class, and so on.

To calculate the cumulative percentage frequency for each class, you would start by adding together the frequencies of all the classes that are less than or equal to the upper bound of the current class. For the 0-9 class, the cumulative percentage frequency would be 10/100 = 10%. For the 10-19 class, the cumulative percentage frequency would be 10 + 20 = 30/100 = 30%. For the 20-29 class, the cumulative percentage frequency would be 30 + 15 = 45/100 = 45%. And so on.

The cumulative percentage frequency distribution is a useful way to visualize and summarize data because it shows the overall pattern of the distribution and allows you to easily compare the frequencies of different ranges. It is often used in statistical analysis and decision-making, as it can help to identify trends and patterns in the data and inform data-driven decision making.

In conclusion, the cumulative percentage frequency distribution is a useful tool for organizing and presenting data in a graphical or tabular format. It shows the percentage of observations that fall within a given range of values and is calculated by adding together the frequencies of all the values that are less than or equal to the upper bound of each range. It is a useful way to visualize and summarize data and can inform decision making by identifying trends and patterns in the data.