Frequency Polygon Calculator
Enter the midpoint and frequency of each class interval to plot a frequency polygon, find the weighted mean, and calculate the standard deviation of your grouped data.
Mean of grouped data: Σ(midpoint × frequency) / Σfrequency
- 1
Total frequency
Σfᵢ = 40 - 2
Weighted sum
Σ(mᵢ × fᵢ) = 940Sum of each class midpoint multiplied by its frequency. - 3
Weighted mean
940 ÷ 40 = 23.500
How does this calculator work?
A frequency polygon plots class midpoints against frequencies and connects them with lines. The weighted mean is Σ(midpoint × frequency) / total frequency. Enter your midpoints and frequencies as comma-separated lists to instantly get the mean, standard deviation, and a visual polygon.
Formula
How this is calculated
A frequency polygon connects the midpoints of class intervals on the x-axis to their frequencies on the y-axis with straight-line segments, giving a visual shape to a frequency distribution. This is the standard way to compare multiple distributions on the same chart.
The weighted mean for grouped data is computed as the sum of each midpoint multiplied by its frequency, divided by the total frequency: mean = Σ(mᵢ·fᵢ) / Σfᵢ. This approximates the true mean because the original individual observations within each class are unknown — we assume they cluster at the midpoint. The standard deviation follows from the population formula applied to the grouped weights.
Limitation: these are estimates, not exact figures, because grouping discards within-class detail. Results improve with narrower class intervals and larger samples.
Frequently asked questions
A histogram uses bars whose area represents frequency; a frequency polygon replaces those bars with points at the midpoints and connects them with straight lines. Polygons are better for overlaying two distributions on one chart, while histograms show the shape more clearly for a single distribution.
Individual data within a class are unknown once grouped, so we use the midpoint as the best single representative value for all observations in that interval. This is a standard approximation in grouped-data statistics.
The accuracy depends on how evenly data are spread within each class. With equal-width classes the estimate is usually very close to the true mean. Skewed within-class distributions can introduce small bias.
Also known as
TG we-Calculate Editorial Team. (2026). Frequency Polygon Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/frequency-polygon-calculator
TG we-Calculate Editorial Team. "Frequency Polygon Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/frequency-polygon-calculator.
TG we-Calculate Editorial Team, "Frequency Polygon Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/frequency-polygon-calculator
@misc{wecalculate_frequency_polygon_calculator, title = {Frequency Polygon Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/frequency-polygon-calculator}}, year = {2026}, note = {TG we-Calculate} }
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