Frequency Polygon for Distribution Comparison — Seaborn

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 Seaborn

Python source (Seaborn)

""" anyplot.ai
frequency-polygon-basic: Frequency Polygon for Distribution Comparison
Library: seaborn 0.13.2 | Python 3.13.13
Quality: 95/100 | Updated: 2026-05-17
"""

import os

import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns


# 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 - first series always #009E73
IMPRINT = ["#009E73", "#C475FD", "#4467A3"]

# Data - Test scores by class
np.random.seed(42)
n_per_group = 200

# Class A: well-distributed performance centered around 75
class_a = np.random.normal(loc=75, scale=12, size=n_per_group)

# Class B: higher achieving class centered around 82
class_b = np.random.normal(loc=82, scale=10, size=n_per_group)

# Class C: bimodal - mix of high performers and struggling students
class_c = np.concatenate(
    [
        np.random.normal(loc=70, scale=11, size=n_per_group // 2),
        np.random.normal(loc=88, scale=9, size=n_per_group // 2),
    ]
)

# Align bin edges across all groups for accurate comparison
all_scores = np.concatenate([class_a, class_b, class_c])
bins = np.linspace(max(0, all_scores.min() - 5), min(100, all_scores.max() + 5), 20)
bin_centers = (bins[:-1] + bins[1:]) / 2

# Compute frequencies for each class (extend to zero at ends for closed polygon)
class_a_counts, _ = np.histogram(class_a, bins=bins)
class_a_x = np.concatenate([[bins[0]], bin_centers, [bins[-1]]])
class_a_y = np.concatenate([[0], class_a_counts, [0]])

class_b_counts, _ = np.histogram(class_b, bins=bins)
class_b_x = np.concatenate([[bins[0]], bin_centers, [bins[-1]]])
class_b_y = np.concatenate([[0], class_b_counts, [0]])

class_c_counts, _ = np.histogram(class_c, bins=bins)
class_c_x = np.concatenate([[bins[0]], bin_centers, [bins[-1]]])
class_c_y = np.concatenate([[0], class_c_counts, [0]])

# Create figure with theme-aware styling
sns.set_theme(
    style="ticks",
    rc={
        "figure.facecolor": PAGE_BG,
        "axes.facecolor": PAGE_BG,
        "axes.edgecolor": INK_SOFT,
        "axes.labelcolor": INK,
        "text.color": INK,
        "xtick.color": INK_SOFT,
        "ytick.color": INK_SOFT,
        "grid.color": INK,
        "grid.alpha": 0.10,
        "legend.facecolor": ELEVATED_BG,
        "legend.edgecolor": INK_SOFT,
    },
)

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

# Plot frequency polygons using seaborn's lineplot
# Class A - Okabe-Ito position 1 (brand green)
sns.lineplot(
    x=class_a_x,
    y=class_a_y,
    ax=ax,
    linewidth=3,
    color=IMPRINT[0],
    label="Class A",
    marker="o",
    markersize=8,
    markevery=slice(1, -1),
)
ax.fill_between(class_a_x, class_a_y, alpha=0.15, color=IMPRINT[0])

# Class B - Okabe-Ito position 2 (vermillion)
sns.lineplot(
    x=class_b_x,
    y=class_b_y,
    ax=ax,
    linewidth=3,
    color=IMPRINT[1],
    label="Class B",
    marker="s",
    markersize=8,
    markevery=slice(1, -1),
)
ax.fill_between(class_b_x, class_b_y, alpha=0.15, color=IMPRINT[1])

# Class C - Okabe-Ito position 3 (blue)
sns.lineplot(
    x=class_c_x,
    y=class_c_y,
    ax=ax,
    linewidth=3,
    color=IMPRINT[2],
    label="Class C",
    marker="^",
    markersize=8,
    markevery=slice(1, -1),
)
ax.fill_between(class_c_x, class_c_y, alpha=0.15, color=IMPRINT[2])

# Styling
ax.set_xlabel("Test Score", fontsize=20, color=INK)
ax.set_ylabel("Frequency", fontsize=20, color=INK)
ax.set_title("frequency-polygon-basic · seaborn · anyplot.ai", fontsize=24, fontweight="medium", color=INK)
ax.tick_params(axis="both", labelsize=16, colors=INK_SOFT)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
for spine in ("left", "bottom"):
    ax.spines[spine].set_color(INK_SOFT)
ax.yaxis.grid(True, alpha=0.10, linewidth=0.8, color=INK)
ax.legend(fontsize=16, loc="upper right", framealpha=0.95, edgecolor=INK_SOFT)
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 — Seaborn

Python source (Seaborn)

Other implementations