Frequency Polygon for Distribution Comparison — Matplotlib

A frequency polygon connects the midpoints of histogram bins with straight line segments, creating a smooth outline of the distribution shape. This visualization excels at comparing multiple distributions simultaneously since lines overlap without obscuring each other, unlike stacked or overlapping histogram bars. Frequency polygons reveal differences in central tendency, spread, skewness, and modality across groups with minimal visual clutter.

Frequency Polygon for Distribution Comparison rendered with Matplotlib

Python source (Matplotlib)

""" anyplot.ai
frequency-polygon-basic: Frequency Polygon for Distribution Comparison
Library: matplotlib 3.10.9 | Python 3.13.13
Quality: 92/100 | Updated: 2026-05-17
"""

import os

import matplotlib.pyplot as plt
import numpy as np


# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"

# Okabe-Ito palette (positions 1-3)
COLORS = ["#009E73", "#C475FD", "#4467A3"]

# Data - Heights by age group
np.random.seed(42)
n_per_group = 200

# Generate three distinct distributions representing height measurements (cm)
young_adults = np.random.normal(loc=172, scale=8, size=n_per_group)
middle_aged = np.random.normal(loc=170, scale=9, size=n_per_group)
seniors = np.random.normal(loc=166, scale=10, size=n_per_group)

groups = [young_adults, middle_aged, seniors]
group_names = ["Young Adults (18-25)", "Middle-Aged (40-50)", "Seniors (65+)"]

# Create common bin edges for all groups
all_data = np.concatenate(groups)
bin_edges = np.linspace(all_data.min() - 5, all_data.max() + 5, 20)
bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2

# Plot
fig, ax = plt.subplots(figsize=(16, 9), facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)

for data, name, color in zip(groups, group_names, COLORS, strict=True):
    # Calculate histogram frequencies
    counts, _ = np.histogram(data, bins=bin_edges)

    # Extend to zero at both ends to close the polygon
    x_extended = np.concatenate([[bin_edges[0]], bin_centers, [bin_edges[-1]]])
    y_extended = np.concatenate([[0], counts, [0]])

    # Plot frequency polygon line
    ax.plot(
        x_extended,
        y_extended,
        linewidth=3,
        color=color,
        label=name,
        marker="o",
        markersize=6,
        markerfacecolor=color,
        markeredgecolor=PAGE_BG,
        markeredgewidth=1,
    )

    # Add semi-transparent fill
    ax.fill(x_extended, y_extended, color=color, alpha=0.15)

# Labels and styling
ax.set_xlabel("Height (cm)", fontsize=20, color=INK)
ax.set_ylabel("Frequency", fontsize=20, color=INK)
ax.set_title("frequency-polygon-basic · matplotlib · anyplot.ai", fontsize=24, fontweight="medium", color=INK)
ax.tick_params(axis="both", labelsize=16, colors=INK_SOFT)

# Spine styling
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
for s in ("left", "bottom"):
    ax.spines[s].set_color(INK_SOFT)

# Grid styling
ax.yaxis.grid(True, alpha=0.10, linewidth=0.8, color=INK)

# Legend with theme-adaptive background
leg = ax.legend(fontsize=16, loc="upper left", framealpha=0.95)
if leg:
    leg.get_frame().set_facecolor(ELEVATED_BG)
    leg.get_frame().set_edgecolor(INK_SOFT)
    leg.get_frame().set_linewidth(0.8)
    for text in leg.get_texts():
        text.set_color(INK_SOFT)

# Ensure y-axis starts at 0
ax.set_ylim(bottom=0)

plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=300, bbox_inches="tight", facecolor=PAGE_BG)

Part of Frequency Polygon for Distribution Comparison on anyplot.ai.

Frequency Polygon for Distribution Comparison — Matplotlib

Python source (Matplotlib)

Other implementations