Visualization Foundations

• ID: DS-L05
• Type: Lesson
• Audience: Beginner / Intermediate
• Theme: Foundational data visualization using clear, reproducible workflows

Visualization is one of the most important tools in data science.

A good plot helps reveal structure, compare groups, identify unusual values, and communicate findings clearly.

But visualization is not only about producing charts.

It is also about learning how to read evidence from patterns.

In this lesson, we focus on foundational plot types that appear in real analytical workflows. We use the wrangled Iris dataset from Chapter 04 so that the visualization step builds on the outputs already produced by the system.

---

Lesson overview

By the end of this lesson, you will be able to:

• create histograms, density plots, ECDF plots, boxplots, violin plots, scatter plots, heatmaps, and pairplots
• compare numeric distributions across groups
• compare alternative figures for the same analytical question
• use color to represent categories clearly
• interpret patterns, spread, overlap, and separation
• save figures as reusable analysis outputs
• run a reusable plotting script from the command line

---

Chapter workflow

This chapter introduces the fourth reusable Python script in the system:

05-visualization-basics.qmd
        ↓
scripts/python/plot_example_data.py
        ↓
data/iris_wrangled.csv
results/figures/
results/figures/figure-index.tsv

The figures produced here support interpretation and reporting in later chapters.

---

Build a visual story

A useful collection of figures should feel like a guided story rather than a random gallery.

In this chapter, the story moves through five questions:

1. What does one variable look like?
2. How do its distributions differ across species?
3. How do groups compare in center, spread, and individual observations?
4. How are two measurements related?
5. What broader multivariable structure is visible?

Different plots can answer the same question from different angles. Showing more than one view is especially valuable when each view reveals something the others hide.

---

Load the wrangled dataset

We use the wrangled dataset prepared in Chapter 04.

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

df = pd.read_csv("data/iris_wrangled.csv")
df.head()

---

Inspect the variables

Before plotting, confirm the structure of the dataset.

print("Shape:", df.shape)
print("\nColumns:", df.columns.tolist())
print("\nData types:")
print(df.dtypes)

Interpretation

Before making plots, ask:

• which variables are numeric?
• which variable defines the groups?
• which comparisons are likely to be meaningful?
• which derived features are available from the wrangling step?

For the Iris dataset, the numeric flower measurements, the derived petal_area, and the categorical species variable support both distribution plots and grouped comparisons.

---

Histogram

Histograms help us understand the distribution of a single numeric variable.

fig, ax = plt.subplots(figsize=(8, 5.5))

sns.histplot(
    data=df,
    x="sepal_length",
    bins=12,
    kde=True,
    ax=ax
)

ax.set_title("Distribution of Sepal Length")
ax.set_xlabel("Sepal Length")
ax.set_ylabel("Count")

plt.show()

Histogram showing the distribution of sepal length in the Iris dataset.

Interpretation

When reading a histogram, look for:

• the center of the distribution
• the spread of values
• skewness
• possible multiple peaks

If a variable shows multiple peaks, this may suggest the presence of meaningful subgroups.

---

Three views of one distribution

A histogram is familiar, but it is not the only way to examine a numeric distribution. The following three-panel figure shows the same sepal_length values as a histogram, a density curve, and an empirical cumulative distribution function (ECDF).

fig, axes = plt.subplots(1, 3, figsize=(15, 4.5))

sns.histplot(data=df, x="sepal_length", bins=12, ax=axes[0])
axes[0].set_title("Histogram")
axes[0].set_ylabel("Count")

sns.kdeplot(data=df, x="sepal_length", fill=True, ax=axes[1])
axes[1].set_title("Density")
axes[1].set_ylabel("Density")

sns.ecdfplot(data=df, x="sepal_length", ax=axes[2])
axes[2].set_title("ECDF")
axes[2].set_ylabel("Proportion at or below")

fig.suptitle("Three Views of Sepal Length", y=1.03)
plt.tight_layout()
plt.show()

Three complementary views of sepal length: histogram, density curve, and ECDF.

Interpretation

• The histogram makes frequencies and possible peaks easy to see, but its appearance depends on the selected bins.
• The density plot emphasizes the overall shape, but smoothing can hide small details.
• The ECDF shows the proportion of observations at or below any value without requiring bins or smoothing.

These are alternatives, not competitors. The best choice depends on the question and the audience.

---

Boxplot

Boxplots summarize a distribution using the median, quartiles, and possible outliers.

fig, ax = plt.subplots(figsize=(8, 5.5))

sns.boxplot(
    data=df,
    x="species",
    y="sepal_length",
    ax=ax
)

ax.set_title("Sepal Length by Species")
ax.set_xlabel("Species")
ax.set_ylabel("Sepal Length")

plt.show()

Boxplot comparing sepal length across the three Iris species.

Interpretation

A boxplot helps compare groups by showing:

• differences in typical values through the median
• variation within each group
• possible outliers
• overlap across groups

If two groups overlap strongly, that variable alone may not separate them well.

---

Scatter plot

Scatter plots show the relationship between two numeric variables.

fig, ax = plt.subplots(figsize=(8, 5.5))

sns.scatterplot(
    data=df,
    x="sepal_length",
    y="petal_length",
    hue="species",
    s=70,
    alpha=0.8,
    ax=ax
)

ax.set_title("Sepal Length vs Petal Length")
ax.set_xlabel("Sepal Length")
ax.set_ylabel("Petal Length")

plt.show()

Scatter plot showing the relationship between sepal length and petal length, colored by species.

Interpretation

Scatter plots help you evaluate:

• whether two variables move together
• whether groups form distinct clusters
• whether the pattern appears linear or non-linear
• whether any observations appear unusual

In many datasets, scatter plots are among the fastest ways to detect group structure.

---

Grouped histogram

A grouped histogram helps compare distributions across categories.

fig, ax = plt.subplots(figsize=(8, 5.5))

sns.histplot(
    data=df,
    x="petal_length",
    hue="species",
    bins=15,
    kde=True,
    ax=ax
)

ax.set_title("Petal Length Distribution by Species")
ax.set_xlabel("Petal Length")
ax.set_ylabel("Count")

plt.show()

Overlaid petal-length distributions for the three Iris species.

Interpretation

This plot helps compare whether groups differ in:

• location
• spread
• overlap
• shape of the distribution

If one group’s values occupy a clearly different range, that variable may be useful for distinguishing between groups.

---

Small-multiple histograms

Overlaid distributions can become crowded. Small multiples give every species its own panel while preserving a common scale.

g = sns.displot(
    data=df,
    x="petal_length",
    col="species",
    col_wrap=3,
    bins=10,
    kde=True,
    height=3.5,
    aspect=1
)

g.set_axis_labels("Petal Length", "Count")
g.set_titles("{col_name}")
g.fig.suptitle("Petal Length Distribution within Each Species", y=1.05)

plt.show()

Small-multiple histograms showing the petal-length distribution within each species.

Interpretation

The grouped histogram is best for seeing overlap directly. The small-multiple version is often easier for comparing the shape and spread within each group. Using both views shows that setosa is clearly separated, while versicolor and virginica retain some overlap.

---

Derived feature plot

Because Chapter 04 created petal_area, we can now visualize it directly.

fig, ax = plt.subplots(figsize=(8, 5.5))

sns.boxplot(
    data=df,
    x="species",
    y="petal_area",
    ax=ax
)

sns.stripplot(
    data=df,
    x="species",
    y="petal_area",
    color="black",
    alpha=0.55,
    size=4,
    jitter=0.22,
    ax=ax
)

ax.set_title("Petal Area by Species")
ax.set_xlabel("Species")
ax.set_ylabel("Petal Area")

plt.show()

Petal area by species, shown with boxplots and individual observations.

Interpretation

This plot connects wrangling to visualization.

A derived feature is only useful if it helps answer a question or clarify a pattern. Here, petal_area gives a compact petal-size measure that separates species more clearly than many sepal-based comparisons.

---

Boxplot and violin plot comparison

Boxplots and violin plots summarize the same grouped distributions in different ways.

fig, axes = plt.subplots(1, 2, figsize=(13, 5.5), sharey=True)

sns.boxplot(data=df, x="species", y="petal_area", ax=axes[0])
axes[0].set_title("Boxplot")
axes[0].set_xlabel("Species")
axes[0].set_ylabel("Petal Area")

sns.violinplot(
    data=df,
    x="species",
    y="petal_area",
    inner="quartile",
    cut=0,
    ax=axes[1]
)
sns.stripplot(
    data=df,
    x="species",
    y="petal_area",
    color="black",
    alpha=0.4,
    size=3,
    jitter=0.16,
    ax=axes[1]
)
axes[1].set_title("Violin Plot with Observations")
axes[1].set_xlabel("Species")
axes[1].set_ylabel("")

fig.suptitle("Two Views of Petal Area by Species", y=1.02)
plt.tight_layout()
plt.show()

Side-by-side boxplot and violin-plot views of petal area by species.

Interpretation

The boxplot gives a compact summary of the median and quartiles. The violin plot reveals the estimated distribution shape, while the overlaid points keep the individual observations visible. For small datasets, displaying the observations helps prevent a smooth distribution from appearing more precise than the data support.

---

Scatter plot with trend lines

The earlier scatter plot emphasizes clusters. Adding a separate trend line for each species helps compare within-group relationships.

g = sns.lmplot(
    data=df,
    x="sepal_length",
    y="petal_length",
    hue="species",
    height=5.5,
    aspect=1.35,
    scatter_kws={"s": 55, "alpha": 0.75},
    ci=None
)

g.set_axis_labels("Sepal Length", "Petal Length")
g.fig.suptitle("Within-Species Trends: Sepal Length vs Petal Length", y=1.03)

plt.show()

Scatter plot with separate within-species trend lines for sepal length and petal length.

Interpretation

The overall upward pattern partly reflects differences between species. Within-species trend lines help separate that group structure from the relationship observed inside each species. A visible overall association does not always mean the same relationship is equally strong within every group.

---

Correlation heatmap

A correlation heatmap provides a compact overview of linear relationships among all numeric features.

numeric_columns = [
    "sepal_length",
    "sepal_width",
    "petal_length",
    "petal_width",
    "petal_area"
]

correlations = df[numeric_columns].corr()

fig, ax = plt.subplots(figsize=(8, 6.5))

sns.heatmap(
    correlations,
    annot=True,
    fmt=".2f",
    cmap="vlag",
    center=0,
    vmin=-1,
    vmax=1,
    square=True,
    ax=ax
)

ax.set_title("Correlation among Iris Numeric Features")
plt.tight_layout()
plt.show()

Annotated correlation heatmap for the numeric Iris features.

Interpretation

Petal length, petal width, and petal area are strongly related. This agrees with the scatter plots and helps identify features that may carry similar information. Correlation summarizes linear association; it does not explain causation or replace inspection of the underlying points.

---

Pairplot overview

Pairplots provide a compact view of multiple variable relationships at once.

g = sns.pairplot(
    df[[
        "sepal_length",
        "sepal_width",
        "petal_length",
        "petal_width",
        "petal_area",
        "species"
    ]],
    hue="species",
    corner=True,
    plot_kws={"alpha": 0.7}
)

g.fig.suptitle("Iris — Pairwise Relationships by Species", y=1.02)

plt.show()

Pairplot showing pairwise relationships among Iris measurements, colored by species.

Interpretation

Pairplots help answer broader questions such as:

• which variables best separate species?
• which features appear strongly related?
• which measurements appear redundant?
• where groups overlap and where they separate clearly?

This is often one of the most useful first multivariate views of a dataset.

---

Reading visual evidence carefully

A plot is only useful if it is interpreted carefully.

When reading a figure, ask:

• what question does this plot help answer?
• what pattern is visible?
• how strong is the pattern?
• is there overlap, uncertainty, or ambiguity?
• does this align with earlier summaries?

Visualization should support reasoning, not replace it.

---

Visualization principles

Strong foundational plots share a few key qualities:

• clear titles and labels
• readable axes
• purposeful use of color
• minimal clutter
• plot choice matched to the question

A histogram is useful for one-variable distributions.
A boxplot is useful for comparing distributions across groups.
A scatter plot is useful for relationships between two variables.
A pairplot is useful for quick multivariate exploration.

---

Validation through visualization

Plots can also function as validation tools.

Use them to check:

• whether distributions look plausible
• whether outliers need review
• whether grouped differences are real or mostly overlap
• whether patterns are consistent with earlier cleaning and wrangling steps

Visualization often reveals issues that summary tables alone can miss.

---

Run the reusable plotting script

The manual plotting examples above explain the logic. The reusable script creates and saves a standard figure set.

Run this from the project root:

python scripts/python/plot_example_data.py data/iris_wrangled.csv results/figures

Expected outputs:

results/figures/
├── histogram-sepal-length.png
├── distribution-views-sepal-length.png
├── boxplot-sepal-length-by-species.png
├── scatter-sepal-length-vs-petal-length.png
├── histogram-petal-length-by-species.png
├── small-multiples-petal-length-by-species.png
├── boxplot-petal-area-by-species.png
├── comparison-petal-area-by-species.png
├── scatter-trends-by-species.png
├── correlation-heatmap.png
├── pairplot-iris-by-species.png
└── figure-index.tsv

---

What the plotting script does

The script:

• reads the wrangled input table
• validates required columns
• creates a varied set of exploratory and comparison figures
• saves figures as .png files
• writes a figure index table with filenames and descriptions

The figure index helps later reporting chapters refer to plots consistently.

---

Exercise

Try the following:

1. Open results/figures/figure-index.tsv.
2. Open results/figures/boxplot-petal-area-by-species.png.
3. Compare the boxplot and violin plot of petal_area.
4. Create a scatter plot of sepal_width versus petal_width.
5. Plot both a histogram and an ECDF of petal_width.
6. Write one sentence describing which figure most clearly shows species separation and explain why.

---

Solution

fig, ax = plt.subplots(figsize=(8, 5.5))

sns.scatterplot(
    data=df,
    x="sepal_width",
    y="petal_width",
    hue="species",
    s=70,
    alpha=0.8,
    ax=ax
)

ax.set_title("Sepal Width vs Petal Width")
ax.set_xlabel("Sepal Width")
ax.set_ylabel("Petal Width")

plt.show()

fig, axes = plt.subplots(1, 2, figsize=(12, 5))

sns.histplot(data=df, x="petal_width", bins=12, ax=axes[0])
axes[0].set_title("Histogram of Petal Width")
axes[0].set_xlabel("Petal Width")
axes[0].set_ylabel("Count")

sns.ecdfplot(data=df, x="petal_width", ax=axes[1])
axes[1].set_title("ECDF of Petal Width")
axes[1].set_xlabel("Petal Width")
axes[1].set_ylabel("Proportion at or below")

plt.tight_layout()
plt.show()

print(
    "The pairplot most clearly shows overall species separation because "
    "it compares several feature combinations in one coordinated view."
)

---

CDI Insight

Visualization is not about producing more plots.

It is about choosing the right view of the data to support understanding.

A clear plot reduces uncertainty. A poor plot can introduce it.

In CDI systems, figures should be reproducible outputs, not temporary screenshots. A saved figure, a figure index, and the script that produced them make visual evidence easier to review and reuse.

---

Summary

In this lesson, you:

• used a varied set of foundational plot types to explore the Iris dataset
• compared multiple visual choices for the same question
• compared distributions within and across species
• examined relationships between numeric variables
• visualized the derived petal_area feature
• used a heatmap and pairplot to inspect multivariable structure
• used visual patterns to support interpretation
• saved reusable figures with plot_example_data.py
• created results/figures/figure-index.tsv

---

Looking Ahead

In the next chapter, we summarize the analysis more formally. The wrangled tables and saved figures produced here become evidence for written interpretation.