Cumulative Frequency and Ogives

What is Cumulative Frequency?

Cumulative frequency is a way to keep a running total of frequencies in a data set. It helps us understand how the frequencies accumulate over a range of values.

For example, if you have a list of test scores, cumulative frequency shows how many students scored up to a certain mark.

How to Calculate Cumulative Frequency

1. List the Frequencies: Start with a frequency distribution table.
2. Add Up: Begin with the first frequency, then add each subsequent frequency to the total of the previous ones.

 

What is an Ogive?

An ogive is a graph that represents cumulative frequency. It is a useful tool for visualizing data and identifying medians, quartiles, and percentiles.

 

Steps to Draw an Ogive

1. Prepare a Cumulative Frequency Table: Calculate the cumulative frequencies for your data set.
2. Plot the Points: On a graph, plot the cumulative frequency against the upper class boundary of each interval.
3. Connect the Points: Draw a smooth curve through the plotted points.

 

Example

Example: Constructing a Cumulative Frequency Table and Ogive

Data: Number of books read by students: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4