A frequency polygon is a type of line graph used in statistics to represent the distribution of a dataset. Unlike a general polygon chart (which displays multivariate data on radial axes), a frequency polygon shows how frequently values in a dataset fall within defined intervals, known as class intervals or bins. The result is a polygon-shaped line chart that gives a visual summary of the data's distribution.

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How a Frequency Polygon Differs from a Histogram

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Both frequency polygons and histograms show the distribution of continuous data, but they differ in visual style. A histogram uses bars to represent each class interval — the height of each bar corresponds to the frequency of values in that interval. A frequency polygon replaces the bars with a line connecting the midpoints of each interval at the corresponding frequency height. The frequency polygon makes it easier to compare multiple distributions on the same chart because overlapping lines are clearer than overlapping bars.

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A frequency polygon connects the midpoints of histogram bars, turning a blocky bar chart into a smooth distributional line.

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How to Construct a Frequency Polygon

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To construct a frequency polygon, first organize your data into a frequency distribution table with class intervals and their corresponding frequencies. Calculate the midpoint of each class interval. Plot each midpoint on the X-axis against its frequency on the Y-axis. Connect the plotted points with straight lines. To close the polygon, add two extra midpoints — one before the first class and one after the last class — both at frequency zero.

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Frequency Polygon vs Ogive

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A frequency polygon shows the frequency of values within each class interval. An ogive (also called a cumulative frequency polygon) shows the cumulative frequency up to the end of each class interval. Ogives are useful for answering questions like 'what percentage of the data falls below a certain value?', while frequency polygons are better for understanding the shape of the overall distribution.

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Reading a Frequency Polygon

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The shape of a frequency polygon reveals important characteristics of the dataset. A symmetric bell-shaped frequency polygon suggests a normal distribution. A right-skewed polygon (tail extending to the right) indicates that most values are concentrated at the lower end with a few very high values. A left-skewed polygon indicates the opposite. A bimodal polygon (two peaks) suggests the data may contain two distinct subgroups.

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Applications of Frequency Polygons

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Frequency polygons are widely used in educational statistics courses, in quality control (to visualize the distribution of manufacturing measurements), in finance (to show the distribution of returns), and in social sciences (to compare distributions across different demographic groups). When multiple distributions need to be compared on the same chart, frequency polygons are preferred over histograms because overlapping lines are easier to distinguish than overlapping bars.

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Creating a Frequency Polygon Online

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PolygonChart.org provides free tools for creating frequency polygon charts from your data. Enter your class intervals and frequencies, and the tool will automatically calculate midpoints, plot the polygon, and allow you to customize colors, axis labels, and export formats. No registration is required.

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