Understanding Box Plots

The Problem Box Plots SolveBox Plots कौन सी समस्या हल करते हैं箱线图解决什么问题

You have 100 house prices. Printing all 100 numbers tells you nothing at a glance. The mean can be pulled up by one mansion. Q1, the median and Q3 help — but that is several numbers to keep in your head.

आपके पास 100 घरों की कीमतें हैं। सारी 100 संख्याएँ छापने से एक नज़र में कुछ पता नहीं चलता। एक बँगला mean को ऊपर खींच सकता है। Q1, median और Q3 मदद करते हैं — पर इतनी संख्याएँ दिमाग़ में रखना मुश्किल है।

你有 100 个房价。把 100 个数全打印出来，一眼看不出任何东西。均值会被一座豪宅拉高。Q1、中位数和 Q3 有帮助 —— 但要同时记住好几个数字。

A box plot (also called a box-and-whisker plot) puts these numbers into one small picture. It shows the median, the spread of the middle 50%, how far the typical values reach, and every outlier — all at once.

Box plot (जिसे box-and-whisker plot भी कहते हैं) इन संख्याओं को एक छोटी तस्वीर में रख देता है। यह median, बीच के 50% का फैलाव, आम values कहाँ तक जाती हैं, और हर outlier — सब एक साथ दिखाता है।

箱线图（也叫箱须图，box-and-whisker plot）把这些数字放进一张小图里。它同时展示中位数、中间 50% 的离散程度、典型值的范围，以及每一个离群点。

Box Plots in Pictures — Understand Before the Mathsतस्वीरों में Box Plots — गणित से पहले समझें图解箱线图 — 先理解，再算数

Anatomy of a Box PlotBox Plot की बनावट箱线图的组成

A box plot is built from the five-number summary — minimum, Q1, median, Q3, maximum — plus the 1.5 × IQR rule for outliers. It has five visible parts:

Box plot five-number summary से बनता है — minimum, Q1, median, Q3, maximum — और outliers के लिए 1.5 × IQR नियम से। इसके पाँच दिखने वाले हिस्से हैं:

箱线图由五数概括（最小值、Q1、中位数、Q3、最大值）加上 1.5 × IQR 离群点规则构成。它有五个可见部分：

Calculating the salary box plot step by stepSalary box plot को step-by-step calculate करना分步计算工资箱线图

Salaries (£k): [32, 33, 34, 48, 49, 51, 72, 75, 78, 95, 120, 380]. We use the same method as Matplotlib and NumPy (linear interpolation).

Salaries (£k): [32, 33, 34, 48, 49, 51, 72, 75, 78, 95, 120, 380]. हम वही तरीका इस्तेमाल करते हैं जो Matplotlib और NumPy करते हैं (linear interpolation)।

工资（£k）：[32, 33, 34, 48, 49, 51, 72, 75, 78, 95, 120, 380]。我们使用与 Matplotlib 和 NumPy 相同的方法（线性插值）。

How to Read a Box PlotBox Plot कैसे पढ़ें如何读懂箱线图

Drawing Box Plots in PythonPython में Box Plots बनाना用 Python 画箱线图

Basic box plot with MatplotlibMatplotlib से basic box plot用 Matplotlib 画基础箱线图

import matplotlib.pyplot as plt
from matplotlib.cbook import boxplot_stats

salaries = [32, 33, 34, 48, 49, 51,
            72, 75, 78, 95, 120, 380]          # £ thousands

fig, ax = plt.subplots(figsize=(10, 3.5))
bp = ax.boxplot(salaries, orientation='horizontal',   # Matplotlib 3.10+
                patch_artist=True, widths=0.5)        # patch_artist lets us fill the box

bp['boxes'][0].set(facecolor='#378add', alpha=0.3)
bp['medians'][0].set(color='#1d9e75', linewidth=2.5)
bp['fliers'][0].set(marker='o', markerfacecolor='none',
                    markeredgecolor='#e24b4a', markersize=8)

ax.set_title('Salary Distribution — Box Plot', fontsize=13)
ax.set_xlabel('Salary (£k)')
ax.set_yticks([])
plt.tight_layout()
plt.show()

# The exact numbers Matplotlib used to draw the plot
s = boxplot_stats(salaries)[0]
print(f"Q1 = {s['q1']}, median = {s['med']}, Q3 = {s['q3']}, IQR = {s['iqr']}")
print(f"Whiskers end at {s['whislo']} and {s['whishi']}")
print(f"Outliers (fliers): {s['fliers'].tolist()}")

boxplot_stats() returns the exact numbers Matplotlib drew — the same values we calculated by hand in Section 3.

boxplot_stats() वही संख्याएँ लौटाता है जिनसे Matplotlib ने plot बनाया — वही values जो हमने Section 3 में हाथ से निकालीं।

boxplot_stats() 返回 Matplotlib 实际绘图用的数字 —— 和我们在第 3 节手算的完全一样。

Comparing several groups side by sideकई groups की साथ-साथ तुलना并排比较多个组

import matplotlib.pyplot as plt
from matplotlib.cbook import boxplot_stats

departments = {
    'Engineering': [65, 72, 78, 85, 90, 95, 68, 74, 82, 88, 150],
    'Marketing':   [45, 48, 52, 55, 58, 61, 65, 47, 53, 60, 110],
    'Sales':       [35, 40, 48, 52, 55, 60, 70, 42, 50, 58, 200],
    'HR':          [38, 42, 44, 46, 48, 50, 52, 43, 47, 49,  90],
}

fig, ax = plt.subplots(figsize=(10, 5))
colors = ['#378add', '#1d9e75', '#ba7517', '#7f77dd']

bp = ax.boxplot(list(departments.values()),
                tick_labels=list(departments.keys()),   # was labels= before 3.9
                patch_artist=True, widths=0.5)

for patch, color in zip(bp['boxes'], colors):
    patch.set(facecolor=color, alpha=0.3)
for median in bp['medians']:
    median.set(color='#1a1d2e', linewidth=2)
for flier in bp['fliers']:
    flier.set(marker='o', markerfacecolor='none',
              markeredgecolor='#e24b4a', markersize=8)

ax.set_title('Salary Distribution by Department', fontsize=13)
ax.set_ylabel('Salary (£k)')
ax.grid(axis='y', alpha=0.3)
plt.tight_layout()
plt.show()

for name, s in zip(departments, boxplot_stats(list(departments.values()))):
    print(f"{name:<12} median {s['med']:>5}  IQR {s['iqr']:>5}  outliers {s['fliers'].tolist()}")

Box plot with seabornseaborn से box plot用 seaborn 画箱线图

import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt

data = {
    'salary': [65,72,78,85,90,95,68,74,82,88,150,
               45,48,52,55,58,61,65,47,53,60,110,
               35,40,48,52,55,60,70,42,50,58,200],
    'dept':   ['Engineering']*11 + ['Marketing']*11 + ['Sales']*11
}
df = pd.DataFrame(data)

fig, ax = plt.subplots(figsize=(10, 5))
sns.boxplot(data=df, x='dept', y='salary',
            hue='dept', legend=False,          # seaborn 0.13+: palette needs hue
            palette=['#378add', '#1d9e75', '#ba7517'],
            width=0.5, linewidth=1.5,
            flierprops=dict(marker='o', markerfacecolor='none',
                            markeredgecolor='#e24b4a', markersize=8), ax=ax)
ax.set_title('Salary Distribution by Department', fontsize=13)
ax.grid(axis='y', alpha=0.3)
plt.tight_layout()
plt.show()

# Same numbers as a table
print(df.groupby('dept')['salary'].quantile([0.25, 0.5, 0.75]).unstack().round(2))

In seaborn 0.13+, passing palette without hue gives a warning, so we set hue='dept', legend=False.

seaborn 0.13+ में hue के बिना palette देने पर warning आती है, इसलिए हम hue='dept', legend=False लगाते हैं।

在 seaborn 0.13+ 中，只传 palette 不传 hue 会发出警告，所以我们设置 hue='dept', legend=False。

Reading Box Plots — Three Real StoriesBox Plots पढ़ना — तीन असली कहानियाँ读箱线图 — 三个真实故事

Story 1 — The reliable machineकहानी 1 — भरोसेमंद machine故事 1 — 靠谱的机器

import numpy as np
import matplotlib.pyplot as plt

machine_a = [19.8, 20.0, 20.1, 19.9, 20.2, 20.0, 19.8, 20.1, 20.0, 19.9]
machine_b = [14.0, 26.0, 18.0, 22.0, 20.0, 28.0, 12.0, 24.0, 16.0, 20.0]

fig, ax = plt.subplots(figsize=(8, 4))
bp = ax.boxplot([machine_a, machine_b],
                tick_labels=['Machine A', 'Machine B'],
                patch_artist=True)

bp['boxes'][0].set(facecolor='#1d9e75', alpha=0.3)
bp['boxes'][1].set(facecolor='#e24b4a', alpha=0.3)

ax.axhline(20, color='#7f77dd', linestyle='--', alpha=0.5, label='Target: 20g')
ax.set_title('Biscuit Weight — Machine A vs Machine B')
ax.set_ylabel('Weight (g)')
ax.legend()
plt.tight_layout()
plt.show()

for name, w in [('A', machine_a), ('B', machine_b)]:
    q1, q3 = np.percentile(w, [25, 75])
    print(f"Machine {name}: mean {np.mean(w):.2f} g, median {np.median(w):.2f} g, "
          f"IQR {q3 - q1:.2f} g, range {min(w)}–{max(w)} g")
print("Outlier dots:", [len(f.get_ydata()) for f in bp['fliers']])

Story 2 — Exam scores of two classesकहानी 2 — दो classes के exam scores故事 2 — 两个班的考试成绩

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(0)
class_a = np.clip(np.random.normal(68, 5, 40), 0, 100)
class_b = np.clip(np.random.normal(65, 18, 40), 0, 100)   # scores can't pass 100

fig, ax = plt.subplots(figsize=(8, 4))
bp = ax.boxplot([class_a, class_b], tick_labels=['Class A', 'Class B'],
                patch_artist=True,
                flierprops=dict(marker='o', markerfacecolor='none',
                                markeredgecolor='#e24b4a', markersize=7))
bp['boxes'][0].set(facecolor='#378add', alpha=0.3)
bp['boxes'][1].set(facecolor='#ba7517', alpha=0.3)
ax.set_title('Exam Score Distribution — Two Classes')
ax.set_ylabel('Score'); ax.set_ylim(0, 110); ax.grid(axis='y', alpha=0.3)
plt.tight_layout(); plt.show()

for name, c, f in [('A', class_a, bp['fliers'][0]), ('B', class_b, bp['fliers'][1])]:
    q1, q2, q3 = np.percentile(c, [25, 50, 75])
    print(f"Class {name}: median {q2:.1f}, IQR {q3 - q1:.1f}, "
          f"outlier dots {np.round(f.get_ydata(), 1).tolist()}")
print("Students on exactly 100 in Class B:", int((class_b == 100).sum()))

Story 3 — Spotting sensor faultsकहानी 3 — Sensor की ख़राबी पकड़ना故事 3 — 发现传感器故障

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(1)
normal = np.random.normal(21, 0.5, 50)        # 50 good readings around 21 °C
faulty = np.append(normal, [35.2, 38.7, 2.1])  # 3 faulty readings

fig, ax = plt.subplots(figsize=(8, 4))
bp = ax.boxplot(faulty, orientation='horizontal', patch_artist=True,
                flierprops=dict(marker='D', markerfacecolor='#e24b4a',
                                markeredgecolor='#e24b4a', markersize=9))
bp['boxes'][0].set(facecolor='#378add', alpha=0.25)
bp['medians'][0].set(color='#1d9e75', linewidth=2)
ax.set_title('Room Temperature — Sensor Readings')
ax.set_xlabel('Temperature (°C)'); ax.set_yticks([])
for x, h in [(2.1, 1.3), (35.2, 1.3), (38.7, 1.42)]:   # stagger labels
    ax.annotate('Faulty reading', xy=(x, 1), xytext=(x, h),
                fontsize=9, color='#e24b4a', ha='center',
                arrowprops=dict(arrowstyle='->', color='#e24b4a'))
plt.tight_layout(); plt.show()

fliers = np.sort(bp['fliers'][0].get_xdata())
print("Outlier dots:", fliers.round(2).tolist())
print(f"Mean with faults {faulty.mean():.2f} °C, without {normal.mean():.2f} °C")
print(f"Median with faults {np.median(faulty):.2f} °C, without {np.median(normal):.2f} °C")

The three faults are caught, and they move the mean (21.23 °C vs 20.99 °C) while the median stays at 20.91 °C. In a real system you would remove these readings only after confirming the sensor fault.

तीनों ख़राबियाँ पकड़ी गईं, और वे mean को हिलाती हैं (21.23 °C vs 20.99 °C) जबकि median 20.91 °C पर रहता है। असली system में आप इन readings को sensor की ख़राबी पक्की होने के बाद ही हटाएँगे।

三个故障都被抓到了。它们改变了均值（21.23 °C vs 20.99 °C），而中位数仍是 20.91 °C。在真实系统中，只有确认传感器故障后才应删除这些读数。

Box Plot vs Histogram — Which to Use?Box Plot vs Histogram — कौन सा इस्तेमाल करें?箱线图 vs 直方图 — 用哪个？

Golden RulesGolden Rules黄金法则