Boxplots & Violin Plots

Anatomy of a Boxplot

import pandas as pd
import numpy as np

# 24 patients across 3 wards — length of stay in days
df = pd.DataFrame({
    'ward':     ['Medical']*8 + ['Surgical']*8 + ['Emergency']*8,
    'los_days': [
        4, 6, 5, 7, 8, 5, 6, 21,   # Medical — one very long outlier (21 days)
        9,11,10,13,12,14,11,10,    # Surgical — tight cluster, no outliers
        1, 2, 1, 3, 1, 2, 15, 18   # Emergency — mostly 1-3 days, two long outliers
    ]
})

# Quick stats to see what we're dealing with
print(df.groupby('ward')['los_days'].describe().round(1))

What just happened?

Three very different stories hidden in numbers: Surgical has the tightest spread (std=1.6) — predictable. Emergency's mean (5.4) is way above its median (2.0) — outliers inflating the average. Medical's max of 21 when the 75th percentile is just 7 — one patient is a massive outlier. Boxplots will make all three patterns impossible to miss.

def boxplot_stats(series, label):
    Q1, median, Q3 = series.quantile([0.25, 0.50, 0.75])
    IQR   = Q3 - Q1
    lower = Q1 - 1.5 * IQR
    upper = Q3 + 1.5 * IQR
    outliers = series[(series < lower) | (series > upper)].tolist()

    print(f"  {label}")
    print(f"    Q1={Q1:.0f}  Median={median:.0f}  Q3={Q3:.0f}  IQR={IQR:.0f}")
    print(f"    Fences: [{lower:.1f}, {upper:.1f}]")
    print(f"    Outliers: {outliers if outliers else 'None'}\n")

print("=== BOXPLOT STATS BY WARD ===\n")
for ward, grp in df.groupby('ward'):
    boxplot_stats(grp['los_days'], ward)

What just happened?

pandas' .quantile() takes a list and returns all three percentiles at once. Fences are simple arithmetic. Emergency has two outliers (15 and 18 days) — they stayed 8× the median. Medical has one (21 days). Surgical has none at all — the most predictable ward in the hospital.

Length of Stay by Ward (days)

Red dots = outliers. Surgical has none — its box sits highest because stays are genuinely longer, not because of outliers.

print("=== BOARD BRIEFING: LENGTH-OF-STAY FINDINGS ===\n")

for ward, grp in df.groupby('ward'):
    s      = grp['los_days']
    Q1     = s.quantile(0.25)
    median = s.median()
    Q3     = s.quantile(0.75)
    mean   = s.mean()
    IQR    = Q3 - Q1
    outliers = s[s > Q3 + 1.5*IQR].tolist()

    print(f"  {ward} Ward")
    print(f"  Typical stay: {Q1:.0f}–{Q3:.0f} days  (median={median:.0f}d, mean={mean:.1f}d)")

    # Flag when mean is misleadingly high due to outliers
    if mean > median * 1.25:
        pct_inflated = (mean/median - 1)*100
        print(f"  ⚠  Mean is {pct_inflated:.0f}% above median — use median for planning, not mean")

    # Report outliers in plain English
    if outliers:
        print(f"  ⚠  {len(outliers)} outlier(s): {outliers} days — "
              f"{max(outliers)/median:.0f}x longer than typical stay")
        print(f"     Action: investigate case complexity and flag for clinical review")
    else:
        print(f"  ✓  No outliers — this ward is suitable for capacity planning based on historical data")

    print()

What just happened?

pandas' .median(), .mean(), and .quantile() run inside a groupby loop. The 25% inflation check flags when the mean is misleading. The outlier list is generated with a single boolean filter.

The critical insight for the operations director: Emergency's mean (5.4 days) is 170% above the median (2 days). If she plans bed capacity using the mean, she overestimates by nearly 3×. The median is the right number. Surgical's near-identical mean and median (11.3 vs 11) means it's safe to plan with either — it's genuinely predictable.

Teacher's Note

The boxplot is one of the best "is my mean trustworthy?" checks you have. If the median line sits far from the centre of the box, or if outlier dots appear above the upper whisker, the mean is being distorted. Always check the boxplot before reporting a mean to a stakeholder.

In a real notebook: seaborn.boxplot(x='ward', y='los_days', data=df) draws the full chart in one line. The statistics underneath are exactly what we computed manually — seaborn just draws the shape automatically.

Up Next · Lesson 30

Correlation Maps

Build and read a full correlation heatmap — and learn what it's actually telling you about your features before you model.