Create frequency polygons with SVG visualization, cumulative ogive overlay, class frequency table, polygon coordinates, and automatic class interval selection.
The frequency polygon calculator turns grouped data into a connected line graph by plotting each class midpoint against its frequency. It is a good fit when you want to compare two distributions on the same axes or see the overall shape of a dataset without the visual weight of bars.
This tool builds class intervals automatically or from your custom settings, then outputs the class table, polygon coordinates, and a cumulative ogive for percentile-style reading. The faint histogram backdrop helps you see how the polygon relates to the grouped counts.
Use it when your data has already been grouped or when you want a cleaner comparison chart than a histogram. The coordinate table is especially useful if you need to recreate the graph in spreadsheet software or a report.
Use a frequency polygon when you want to compare grouped distributions without overlapping bars. The chart highlights where class frequencies rise and fall, while the ogive makes it easy to approximate cumulative thresholds such as medians and percentiles.
This calculator is useful for classed survey data, exam score summaries, and any dataset where the grouped shape matters more than individual raw values.
Frequency polygon: plot (class midpoint, frequency) for each class, connected by straight lines. Anchor points at zero frequency are added one class width before the first and after the last class. Ogive: plot (upper class boundary, cumulative frequency).
Result: 5 classes, polygon peaks at midpoint 79.8 with frequency 5
Using Sturges' rule: k = 5 classes, width = 6. The polygon starts and ends at frequency 0 (anchor points), rises to a peak in the middle class, and shows the distribution shape. The ogive curve rises from 0 to 15 (total n).
The calculator first groups the raw numbers into class intervals, then uses each class midpoint as the x-value and the class frequency as the y-value. Connecting those midpoint pairs produces the polygon. Anchor points at zero frequency are added at both ends so the line returns to the baseline.
The ogive is the cumulative version of the same grouped data. Each point shows how many observations are at or below the upper boundary of a class. That makes it a quick way to estimate medians, quartiles, and other cumulative thresholds without sorting the original list by hand.
Frequency polygons are most helpful when you want a compact comparison chart for classroom datasets, grouped survey results, or test-score distributions. They stay readable when you overlay multiple series, which is where histograms become visually crowded.
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A frequency polygon is a line graph of a frequency distribution. Each class is represented by its midpoint on the x-axis and its frequency on the y-axis, with points connected by straight lines. It shows the distribution shape similarly to a histogram but as a continuous line rather than bars.
A histogram uses bars whose widths span class intervals and heights represent frequency. A frequency polygon uses points at class midpoints connected by lines. Polygons are better for comparing multiple distributions (you can overlay lines) and for showing continuous distribution shapes.
Anchor points are zero-frequency points added one class width before the first class and one class width after the last class. They ensure the polygon starts and ends at the x-axis, creating a closed shape whose area equals the total area of the histogram bars. This is mathematically important for area-based interpretations.
An ogive (cumulative frequency polygon) plots cumulative frequency against the upper class boundary. For a normal distribution, it forms an S-shaped curve. You can read approximate percentiles from the ogive: the x-value where the curve reaches 50% of total frequency approximates the median.
Frequency polygons connect class midpoints with straight lines — they depend on the class intervals you choose. Density plots (kernel density estimates) use smoothing to create a continuous curve independent of binning. Use polygons for clear, reproducible class-based visualization. Use density plots for smooth, flexible distribution estimation.
Yes — this is the primary advantage of frequency polygons over histograms. To compare distributions, simply plot multiple polygons on the same axes (same class intervals). Polygons with lines don't overlap like histogram bars do, making comparison clearer.