Cumulative Frequency Distribution

A cumulative frequency distribution is a statistical tool that shows the total number of observations or data points that fall within a certain range or below a specific value. It helps in analyzing and understanding the distribution and spread of the data by presenting the accumulated frequencies.

Key Components

• Data Points: The individual values or observations in a dataset.
• Frequency: The number of occurrences of a particular data point. It represents how frequently a value occurs.
• Cumulative Frequency: The sum of frequencies for all values up to a certain point in the dataset. It involves adding up the frequencies as we move from the lowest to the highest values.

Construction

To create a cumulative frequency distribution, follow these steps:

1. Arrange the data points in ascending order.
2. Determine the frequency of each data point.
3. Calculate the cumulative frequencies by summing up the frequencies in sequence.

Representation

A cumulative frequency distribution can be presented in the form of a table or a graph, called a cumulative frequency curve or an ogive. The graph includes the cumulative frequencies on the y-axis and the data values on the x-axis.

Uses

The cumulative frequency distribution is useful in analyzing data and extracting meaningful insights. It provides information about the spread, central tendency, and distribution of the dataset. Some common applications include:

• Identifying the median and quartiles of a dataset.
• Determining the percentage of data falling within certain intervals.
• Comparing and contrasting different datasets.