Build a frequency polygon from your grouped data by entering class midpoints and their corresponding frequencies. The calculator plots the distribution as a line graph, computes mean, total frequency, and number of classes, and renders a visual chart — giving you a clear snapshot of how your data is distributed.
Total Frequency (n)
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Number of Classes
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Estimated Mean
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Modal Class Midpoint
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Highest Frequency
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A frequency polygon is a line graph used to represent a frequency distribution. It is constructed by plotting the midpoints of each class interval on the X-axis against their corresponding frequencies on the Y-axis, then connecting the plotted points with straight lines. It gives a clear visual picture of the shape of a distribution.
To construct a frequency polygon, first create a frequency distribution table with class intervals and their frequencies. Find the midpoint of each class, plot (midpoint, frequency) as points on a graph, then connect consecutive points with straight lines. The polygon is typically closed by extending to adjacent midpoints with zero frequency at both ends.
A histogram represents frequencies using rectangular bars for each class interval, while a frequency polygon connects the midpoints of those bars with a continuous line. Both convey the same distribution data, but the frequency polygon is better for comparing two or more distributions on the same graph since the lines don't obscure each other the way bars do.
An ogive (also called a cumulative frequency polygon) is a line graph that plots cumulative frequencies against class midpoints or upper class boundaries. It shows how frequencies accumulate across classes and is useful for determining medians, quartiles, and percentiles from grouped data.
The peak of the polygon indicates the class with the highest frequency (the modal class). The overall shape reveals whether the distribution is symmetric, skewed left, or skewed right. A wider spread suggests greater variability in the data, while a narrow, tall peak indicates data concentrated around a central value.
The estimated mean from grouped data is calculated as the sum of (midpoint × frequency) for all classes, divided by the total frequency. This calculator computes this automatically once you enter your midpoints and frequencies.
Yes — one of the key advantages of frequency polygons over histograms is that multiple polygons can be overlaid on the same axes for easy visual comparison. This is especially useful in statistics for comparing the distributions of two different groups or datasets.
The modal class is the class interval with the highest frequency. Its midpoint is reported in this calculator as the Modal Class Midpoint. In a frequency polygon, the modal class corresponds to the highest peak of the line graph.