October 11, 2025

What Is A Cumulative Frequency Graph

Q: What is the difference between a frequency graph and a cumulative frequency graph?

A frequency graph (like a histogram) displays the frequency of data points within specific intervals, while a cumulative frequency graph shows the running total of frequencies, indicating the number of data points falling below the upper limit of each interval.

Q: What are ogives primarily used for in statistics?

Ogive graphs are primarily used to graphically estimate the median, quartiles, and percentiles of a dataset, providing a visual representation of how data values are distributed and accumulated.

Q: Can a cumulative frequency graph ever go down?

No, a cumulative frequency graph can never decrease. Since it represents an accumulation of frequencies, the line will always either rise or remain flat, reflecting that the number of observations up to a certain point cannot decrease.

Q: How do you find the interquartile range using an ogive?

To find the interquartile range (IQR), first locate Q1 (25th percentile) and Q3 (75th percentile) on the cumulative frequency axis. Draw horizontal lines from these points to the ogive, then vertical lines down to the data axis. The difference between the data values at Q3 and Q1 is the estimated interquartile range.

A cumulative frequency graph, also known as an ogive, visually displays the running total of frequencies for data, helping to determine how many data points fall below a certain value and estimate statistical measures.

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Definition of a Cumulative Frequency Graph

A cumulative frequency graph, commonly referred to as an ogive, is a statistical chart that shows the running total of frequencies in a dataset. It illustrates how many observations or data points fall below a specific value, making it easier to understand the distribution of data over its range.

How it's Constructed

To build an ogive, data is first organized into a frequency distribution table, including class intervals and their corresponding frequencies. A cumulative frequency column is then added, where each entry is the sum of its frequency and all preceding frequencies. These cumulative frequencies are then plotted against the upper class boundaries of their respective intervals, typically forming a smooth, non-decreasing curve.

A Practical Example

Consider the heights of students in a class. If 5 students are between 140-150 cm, 10 are 151-160 cm, and 7 are 161-170 cm. The cumulative frequencies would be: 5 (less than 150.5 cm), 15 (less than 160.5 cm), and 22 (less than 170.5 cm). Plotting these cumulative counts against the upper boundaries (150.5, 160.5, 170.5) generates the cumulative frequency graph, clearly showing, for instance, that 15 students are shorter than 160.5 cm.

Importance and Applications

Cumulative frequency graphs are invaluable tools for quickly estimating key statistical measures such as the median, quartiles (Q1, Q2, Q3), and percentiles directly from grouped data. They provide a clear visual summary of data distribution, aiding in various fields like educational assessment, public health research, and market analysis to identify trends and make informed decisions.

Frequently Asked Questions

What is the difference between a frequency graph and a cumulative frequency graph?

What are ogives primarily used for in statistics?

Can a cumulative frequency graph ever go down?

How do you find the interquartile range using an ogive?