Distributions Histograms Density Plots

Why this matters

Understanding distributions shows how your data is actually shaped, not just its average. As a Data Analyst, you will:

• Check if a metric is skewed before reporting a mean (e.g., order values, session duration).
• Pick the right summary (median vs mean) and detect outliers quickly.
• Compare groups (A/B variants, regions) to see real shifts, not noise.
• Communicate uncertainty and typical ranges clearly to stakeholders.

Who this is for

Beginner to intermediate analysts who need to visualize data distributions and interpret them for real decisions.

Prerequisites

• Basic descriptive statistics: mean, median, percentiles.
• Comfort loading data into a tool (spreadsheets, Python, or SQL client).
• Basic plotting knowledge helps but is not required.

Concept explained simply

A histogram counts how many values fall into each numeric interval (bin). A density plot is a smooth curve estimating how common values are across the range. Both show shape: center, spread, skew, and multimodality (multiple peaks).

Key choices: bins and bandwidth

• Histogram bins: too few bins hide detail; too many bins add noise. Try 8–30 bins depending on sample size. For n ~ 200–2000, start with 15–25 bins.
• Density bandwidth: too small shows spiky noise; too large oversmooths. Start with defaults, then adjust until main shape is clear without jaggedness.

How to read histograms vs density plots

• Center: where most values cluster (peak area). Median is near the midpoint of area; mean pulls toward the tail.
• Spread: how wide the mass of data stretches (IQR for middle 50%).
• Skew: long tail to the right (right-skew) or left (left-skew).
• Peaks: one peak (unimodal) or several peaks (multimodal) may indicate subgroups.
• Outliers: isolated bars/long tails that may need investigation.

Worked examples

Example 1: E-commerce order values

Scenario: 5,000 orders; most are small, a few are very large.

• Plot: Histogram with density overlay.
• Observation: Strong right-skew. Median around $32; mean around $58 due to a tail of high spenders.
• Decision: Report median for “typical order” and show 90th percentile to acknowledge big spenders.

Example 2: Session duration (minutes)

Scenario: 2,000 sessions.

• Plot: Histogram with 20 bins, density on top.
• Observation: Peak at 3–5 minutes, gradual right tail up to ~40 minutes.
• Decision: Use median duration in dashboards; show distribution to UX to understand typical vs power users.

Example 3: A/B test conversion lift (user-level deltas)

Scenario: Distribution of per-user spend change vs baseline.

• Plot: Overlaid densities for Variant A and B.
• Observation: Both right-skewed. B shows a slight overall shift right but larger variance.
• Decision: Report median lift and compare quantiles; caution stakeholders about volatile tail behavior.

How to make these plots in common tools

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

# df['value'] is your numeric series
ax = sns.histplot(df['value'], bins=20, stat='density', kde=True, color='#4e79a7')
ax.set_xlabel('Value'); ax.set_ylabel('Density')
plt.show()

-- Generic binning by width (example: 5-unit bins)
SELECT FLOOR(value/5)*5 AS bin_start,
       COUNT(*) AS n
FROM your_table
WHERE value IS NOT NULL
GROUP BY 1
ORDER BY 1;

Common mistakes and self-check

• Mistake: Using mean only on a skewed metric. Fix: Show distribution; add median and percentiles.
• Mistake: Too few or too many bins. Fix: Try several; pick the one that makes primary shape clear without jagged noise.
• Mistake: Comparing groups with different scales (counts). Fix: Use density/relative frequency to compare shapes fairly.
• Mistake: Ignoring outliers. Fix: Show with capped x-axis and note outlier counts separately.
• Mistake: Over-interpreting tiny bumps. Fix: Confirm with sample size; smooth or aggregate if needed.

Exercises

Do these hands-on tasks. Then take the Quick Test. Note: Anyone can take the test for free; only logged-in users will have their progress saved.

Mini challenge

You have two product categories with revenue per order. Category A shows two peaks; Category B shows a single peak with a long right tail. In 3 bullet points, explain what this suggests about customer segments and how you’d present typical revenue to stakeholders for each category.

Practical projects

• Customer spend distribution dashboard: histogram + density, median, p90, and outlier notes.
• Engagement shape report: compare session durations by acquisition channel with normalized densities.
• A/B distribution shift study: visualize control vs variant; report median shift and changes in IQR.

Learning path

1. Distributions (this lesson): shapes, skew, peaks, outliers.
2. Boxplots and percentiles: fast comparisons across many groups.
3. Robust summaries: median, IQR, trimmed mean, Winsorization.
4. Transformation tactics: log scale for heavy tails; when and why.
5. Inference basics: how distribution shape affects tests and confidence intervals.

Next steps

• Recreate two plots from recent work data and present 1-slide insights.
• Adopt a standard: always pair a key metric with its distribution in reports.
• Move on to boxplots and outlier detection to compare many groups quickly.