A boxen plot (also known as letter-value plot) extends the traditional box plot to show more quantile information, making it ideal for large datasets with 1000+ observations. Instead of just displaying the median and quartiles, it shows additional "letter values" (eighths, sixteenths, etc.) as nested boxes, revealing the full shape of the distribution including tail behavior. This makes outlier detection more meaningful and distribution comparison more detailed.
""" anyplot.ai
boxen-basic: Basic Boxen Plot (Letter-Value Plot)
Library: plotly 6.7.0 | Python 3.13.13
Quality: 91/100 | Updated: 2026-05-17
"""
import os
import sys
# Prioritize venv's site-packages over current directory
if sys.prefix not in sys.path:
import site
site_packages = site.getsitepackages()
if isinstance(site_packages, list):
sys.path = site_packages + sys.path
else:
sys.path.insert(0, site_packages)
import numpy as np
import plotly.graph_objects as go
# 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"
GRID = "rgba(26,26,23,0.10)" if THEME == "light" else "rgba(240,239,232,0.10)"
BRAND = "#009E73"
# Data - Server response times by endpoint (large dataset for boxen plot)
np.random.seed(42)
endpoints = ["API Gateway", "Auth Service", "Data Query", "File Upload"]
n_points = 5000
# Generate different distributions for each endpoint
data = {
"API Gateway": np.concatenate(
[
np.random.lognormal(mean=4, sigma=0.5, size=int(n_points * 0.9)),
np.random.uniform(200, 500, size=int(n_points * 0.1)),
]
),
"Auth Service": np.random.exponential(scale=30, size=n_points) + 10,
"Data Query": np.concatenate(
[
np.random.normal(loc=100, scale=20, size=int(n_points * 0.7)),
np.random.normal(loc=250, scale=30, size=int(n_points * 0.3)),
]
),
"File Upload": np.concatenate(
[
np.random.gamma(shape=2, scale=50, size=int(n_points * 0.85)),
np.random.uniform(400, 800, size=int(n_points * 0.15)),
]
),
}
# Colors for quantile levels - theme-adaptive brand green with varying opacity
colors = [
f"rgba({int(BRAND[1:3], 16)}, {int(BRAND[3:5], 16)}, {int(BRAND[5:7], 16)}, 1.0)",
f"rgba({int(BRAND[1:3], 16)}, {int(BRAND[3:5], 16)}, {int(BRAND[5:7], 16)}, 0.85)",
f"rgba({int(BRAND[1:3], 16)}, {int(BRAND[3:5], 16)}, {int(BRAND[5:7], 16)}, 0.7)",
f"rgba({int(BRAND[1:3], 16)}, {int(BRAND[3:5], 16)}, {int(BRAND[5:7], 16)}, 0.55)",
f"rgba({int(BRAND[1:3], 16)}, {int(BRAND[3:5], 16)}, {int(BRAND[5:7], 16)}, 0.4)",
f"rgba({int(BRAND[1:3], 16)}, {int(BRAND[3:5], 16)}, {int(BRAND[5:7], 16)}, 0.3)",
f"rgba({int(BRAND[1:3], 16)}, {int(BRAND[3:5], 16)}, {int(BRAND[5:7], 16)}, 0.2)",
]
fig = go.Figure()
box_width_base = 0.7
positions = list(range(len(endpoints)))
n_levels = 7 # Number of letter value levels
for idx, endpoint in enumerate(endpoints):
pos = positions[idx]
values = data[endpoint]
n = len(values)
sorted_vals = np.sort(values)
median = np.median(values)
# Compute letter values (quantiles at 1/2, 1/4, 1/8, 1/16, etc.)
letter_values = []
for i in range(n_levels):
depth = 2 ** (i + 1)
lower_idx = max(0, min(int(n / depth), n - 1))
upper_idx = max(0, min(int(n - n / depth), n - 1))
letter_values.append((sorted_vals[lower_idx], sorted_vals[upper_idx]))
# Draw boxes from outermost (widest, lightest) to innermost (narrowest, darkest)
for i in range(n_levels - 1, -1, -1):
lower, upper = letter_values[i]
width = box_width_base * (1 - i * 0.15) # Increased from 0.10 to 0.15 for more pronounced decrease
fig.add_shape(
type="rect",
x0=pos - width / 2,
x1=pos + width / 2,
y0=lower,
y1=upper,
fillcolor=colors[i],
line={"color": INK_SOFT, "width": 1.5},
layer="below",
)
# Add median line
fig.add_shape(
type="line",
x0=pos - box_width_base / 2,
x1=pos + box_width_base / 2,
y0=median,
y1=median,
line={"color": INK, "width": 5},
)
# Find and plot outliers (beyond the outermost letter value)
outer_lower, outer_upper = letter_values[-1]
outliers = values[(values < outer_lower) | (values > outer_upper)]
if len(outliers) > 0:
outlier_sample = outliers if len(outliers) <= 100 else np.random.choice(outliers, 100, replace=False)
jitter = np.random.uniform(-0.08, 0.08, size=len(outlier_sample))
fig.add_trace(
go.Scatter(
x=pos + jitter,
y=outlier_sample,
mode="markers",
marker={"color": BRAND, "size": 11, "opacity": 0.7},
showlegend=False,
hovertemplate="Response: %{y:.0f}ms<extra></extra>",
)
)
# Add legend entries for quantile levels
quantile_labels = ["50% (IQR)", "75%", "87.5%", "93.75%", "96.9%", "98.4%", "99.2%"]
for i, label in enumerate(quantile_labels):
fig.add_trace(
go.Scatter(
x=[None],
y=[None],
mode="markers",
marker={"size": 20, "color": colors[i], "symbol": "square", "line": {"color": INK_SOFT, "width": 1}},
name=label,
showlegend=True,
)
)
# Add median legend entry
fig.add_trace(
go.Scatter(x=[None], y=[None], mode="lines", line={"color": INK, "width": 5}, name="Median", showlegend=True)
)
# Layout
fig.update_layout(
title={
"text": "boxen-basic · plotly · anyplot.ai",
"font": {"size": 28, "color": INK},
"x": 0.5,
"xanchor": "center",
},
xaxis={
"title": {"text": "Server Endpoint", "font": {"size": 22, "color": INK}},
"tickfont": {"size": 18, "color": INK_SOFT},
"tickvals": positions,
"ticktext": endpoints,
"showgrid": False,
"zeroline": False,
"linecolor": INK_SOFT,
},
yaxis={
"title": {"text": "Response Time (ms)", "font": {"size": 22, "color": INK}},
"tickfont": {"size": 18, "color": INK_SOFT},
"gridcolor": GRID,
"gridwidth": 1,
"zeroline": False,
"linecolor": INK_SOFT,
},
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
legend={
"title": {"text": "Quantile Level", "font": {"size": 20, "color": INK}},
"font": {"size": 18, "color": INK_SOFT},
"x": 0.98,
"y": 0.5,
"xanchor": "right",
"yanchor": "middle",
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
margin={"l": 120, "r": 220, "t": 100, "b": 100},
)
# Save as PNG and HTML
fig.write_image(f"plot-{THEME}.png", width=1600, height=900, scale=3)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Basic Boxen Plot (Letter-Value Plot) on anyplot.ai.