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.
""" anyplot.ai
frequency-polygon-basic: Frequency Polygon for Distribution Comparison
Library: bokeh 3.9.0 | Python 3.13.13
Quality: 91/100 | Updated: 2026-05-17
"""
import os
import time
from pathlib import Path
import numpy as np
from bokeh.io import output_file, save
from bokeh.models import ColumnDataSource
from bokeh.plotting import figure
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
# 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
IMPRINT = ["#009E73", "#C475FD", "#4467A3"]
# Data - Three groups with different distributions
np.random.seed(42)
# Group A: Normal distribution centered at 65 (Morning Session)
group_a = np.random.normal(loc=65, scale=8, size=300)
# Group B: Normal distribution centered at 75, more spread (Afternoon Session)
group_b = np.random.normal(loc=75, scale=12, size=300)
# Group C: Slightly bimodal distribution (Evening Session)
group_c = np.concatenate([np.random.normal(loc=50, scale=6, size=150), np.random.normal(loc=60, scale=6, size=150)])
# Common bin edges for all groups
all_data = np.concatenate([group_a, group_b, group_c])
bins = np.linspace(all_data.min() - 5, all_data.max() + 5, 21)
bin_centers = (bins[:-1] + bins[1:]) / 2
# Compute histogram counts
counts_a, _ = np.histogram(group_a, bins=bins)
counts_b, _ = np.histogram(group_b, bins=bins)
counts_c, _ = np.histogram(group_c, bins=bins)
# Extend to zero at both ends for closed polygon shape
bin_width = bins[1] - bins[0]
x_extended = np.concatenate([[bin_centers[0] - bin_width], bin_centers, [bin_centers[-1] + bin_width]])
y_a_extended = np.concatenate([[0], counts_a, [0]])
y_b_extended = np.concatenate([[0], counts_b, [0]])
y_c_extended = np.concatenate([[0], counts_c, [0]])
# Create figure
p = figure(
width=4800,
height=2700,
title="frequency-polygon-basic · bokeh · anyplot.ai",
x_axis_label="Test Score (points)",
y_axis_label="Frequency (count)",
)
# Create sources
source_a = ColumnDataSource(data={"x": x_extended, "y": y_a_extended})
source_b = ColumnDataSource(data={"x": x_extended, "y": y_b_extended})
source_c = ColumnDataSource(data={"x": x_extended, "y": y_c_extended})
# Plot frequency polygons with fills
# Group A - Okabe-Ito 1 (Morning Session)
p.patch(x="x", y="y", source=source_a, fill_alpha=0.25, fill_color=IMPRINT[0], line_width=0)
p.line(x="x", y="y", source=source_a, line_color=IMPRINT[0], line_width=3, legend_label="Morning Session")
p.scatter(x=bin_centers, y=counts_a, size=15, color=IMPRINT[0], alpha=0.9)
# Group B - Okabe-Ito 2 (Afternoon Session)
p.patch(x="x", y="y", source=source_b, fill_alpha=0.25, fill_color=IMPRINT[1], line_width=0)
p.line(x="x", y="y", source=source_b, line_color=IMPRINT[1], line_width=3, legend_label="Afternoon Session")
p.scatter(x=bin_centers, y=counts_b, size=15, color=IMPRINT[1], alpha=0.9)
# Group C - Okabe-Ito 3 (Evening Session)
p.patch(x="x", y="y", source=source_c, fill_alpha=0.25, fill_color=IMPRINT[2], line_width=0)
p.line(x="x", y="y", source=source_c, line_color=IMPRINT[2], line_width=3, legend_label="Evening Session")
p.scatter(x=bin_centers, y=counts_c, size=15, color=IMPRINT[2], alpha=0.9)
# Theme-adaptive styling
p.background_fill_color = PAGE_BG
p.border_fill_color = PAGE_BG
p.outline_line_color = INK_SOFT
p.title.text_color = INK
p.title.text_font_size = "28pt"
p.xaxis.axis_label_text_color = INK
p.yaxis.axis_label_text_color = INK
p.xaxis.axis_label_text_font_size = "22pt"
p.yaxis.axis_label_text_font_size = "22pt"
p.xaxis.major_label_text_color = INK_SOFT
p.yaxis.major_label_text_color = INK_SOFT
p.xaxis.major_label_text_font_size = "18pt"
p.yaxis.major_label_text_font_size = "18pt"
p.xaxis.axis_line_color = INK_SOFT
p.yaxis.axis_line_color = INK_SOFT
p.xaxis.major_tick_line_color = INK_SOFT
p.yaxis.major_tick_line_color = INK_SOFT
p.xgrid.grid_line_color = INK
p.ygrid.grid_line_color = INK
p.xgrid.grid_line_alpha = 0.10
p.ygrid.grid_line_alpha = 0.10
# Legend styling
p.legend.location = "top_right"
p.legend.background_fill_color = ELEVATED_BG
p.legend.border_line_color = INK_SOFT
p.legend.label_text_color = INK_SOFT
p.legend.label_text_font_size = "18pt"
p.legend.padding = 15
p.legend.spacing = 8
p.legend.glyph_height = 35
p.legend.glyph_width = 35
p.legend.margin = 20
# Save HTML
output_file(f"plot-{THEME}.html")
save(p)
# Screenshot with headless Chrome
W, H = 4800, 2700
opts = Options()
for arg in (
"--headless=new",
"--no-sandbox",
"--disable-dev-shm-usage",
"--disable-gpu",
f"--window-size={W},{H}",
"--hide-scrollbars",
):
opts.add_argument(arg)
driver = webdriver.Chrome(options=opts)
driver.set_window_size(W, H)
driver.get(f"file://{Path(f'plot-{THEME}.html').resolve()}")
time.sleep(3)
driver.save_screenshot(f"plot-{THEME}.png")
driver.quit()
Part of Frequency Polygon for Distribution Comparison on anyplot.ai.