05 · Data Visualization Basics¶

A well-chosen chart answers a question in half a second that a table of numbers would take a minute to explain. This module covers the four chart types that cover most data science needs — histogram, scatter, bar, and box plot — using matplotlib and seaborn.

Setup and sample data¶

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

rng = np.random.default_rng(3)
n = 200
df = pd.DataFrame({
    "age": rng.integers(18, 70, n),
    "income": rng.normal(45000, 12000, n),
    "region": rng.choice(["North", "South", "East", "West"], n),
    "spend": rng.normal(120, 40, n),
})
df["spend"] = df["spend"] + df["income"] * 0.001  # correlate spend with income a bit

Histogram — the shape of one numeric column¶

Use a histogram whenever the question is "what does the distribution of this column look like?" — is it roughly bell-shaped, skewed, bimodal?

fig, ax = plt.subplots(figsize=(6, 4))
ax.hist(df["income"], bins=20)
ax.set_title("Income distribution")
fig.savefig("income_hist.png", dpi=150)

print(df["income"].min(), df["income"].max())

17651.68 75600.42

Running this produces a bell-shaped histogram centered near $45,000 (matching the rng.normal(45000, 12000, n) generator), ranging from about $17,650 to $75,600 — no long tail or second hump, so a mean/std summary is a reasonable way to describe this column (unlike the income data in Module 04, which had planted outliers that would make a histogram visibly skewed).

Scatter plot — the relationship between two numeric columns¶

Use a scatter plot to see whether two numeric columns move together, and what shape that relationship has (linear, curved, no pattern).

fig, ax = plt.subplots(figsize=(6, 4))
ax.scatter(df["income"], df["spend"], alpha=0.5)
ax.set_xlabel("income")
ax.set_ylabel("spend")
fig.savefig("income_vs_spend.png", dpi=150)

print(df["income"].corr(df["spend"]).round(3))

0.182

The cloud of points slopes gently upward — matching the correlation of 0.182 computed the same way Module 04 introduced. alpha=0.5 (partial transparency) is worth using by default on scatter plots: with 200+ points, overlapping markers otherwise hide how dense a region really is.

Bar chart — comparing a summary statistic across categories¶

Use a bar chart for "compare this number across groups" — never for raw individual data points (that's what a scatter or box plot is for).

fig, ax = plt.subplots(figsize=(6, 4))
df.groupby("region")["spend"].mean().plot(kind="bar", ax=ax)
fig.savefig("spend_by_region.png", dpi=150)

print(df.groupby("region")["spend"].mean().round(1))

region
East     162.2
North    168.9
South    175.9
West     178.5
Name: spend, dtype: float64

The resulting bar chart shows four bars of similar height (162–179), which correctly conveys "spend is fairly similar across regions, with West slightly highest" — the bars all being roughly the same height is the finding.

The most common misleading chart: a truncated y-axis

If that bar chart's y-axis started at 150 instead of 0, the same data would visually scream "West spends dramatically more!" — a real, common trick (intentional or not) for making a small difference look large. Bar charts should almost always start their axis at zero. Line charts showing change over time are a legitimate exception where zooming in is fine, as long as the axis is clearly labeled.

Box plot — distribution comparison across categories¶

A box plot shows the median, IQR (the box), and outliers (the dots) for a numeric column, split by category — it's the "histogram + groupby" combined into one chart.

fig, ax = plt.subplots(figsize=(6, 4))
sns.boxplot(data=df, x="region", y="income", ax=ax)
fig.savefig("income_by_region_box.png", dpi=150)

The box for each region sits at roughly the same height with similar spread — consistent with income being generated independently of region in this synthetic dataset, and a good check against the bar chart above (which only showed the mean of spend, not the full income distribution per region).

Choosing the right chart¶

Question	Chart
What's the shape of one numeric column's distribution?	Histogram
Do two numeric columns move together?	Scatter plot
Compare one summary number across categories	Bar chart
Compare a full distribution across categories	Box plot
How does a value change over time?	Line chart
What fraction does each category make up?	Bar chart (avoid pie charts — humans are bad at comparing angles)

Cheat sheet¶

Task	Code
Histogram	`ax.hist(df["col"], bins=20)`
Scatter	`ax.scatter(df["x"], df["y"], alpha=0.5)`
Bar of a groupby	`df.groupby("g")["v"].mean().plot(kind="bar")`
Box plot by category	`sns.boxplot(data=df, x="cat", y="num")`
Always label axes	`ax.set_xlabel(...)`, `ax.set_ylabel(...)`
Save a figure	`fig.savefig("name.png", dpi=150)`

How It Actually Works¶

How a histogram actually turns numbers into bar heights. bins=20 divides the observed range (min to max) into 20 equal-width intervals, then counts how many values fall into each interval — the bar height is that count (or, if density=True, the count rescaled so the total area under all bars sums to 1, which makes histograms of different sample sizes visually comparable). Bin width matters more than it looks: too few bins smooth away real structure like a second hump (bimodality); too many bins turn sampling noise into what looks like meaningful jaggedness. There's no universally correct bin count — but a common rule of thumb (Sturges' rule, k ≈ log₂(n) + 1) gives a reasonable starting point pandas/matplotlib approximate by default.

Why truncating a y-axis distorts perception, mechanically. A chart communicates magnitude through the visual length of a bar or the slope of a line, both computed as (pixel_height_of_max - pixel_height_of_min) mapped linearly onto the axis range you set. If four bars have values 162–179 mapped onto a 0–200 axis, their pixel-height differences are small relative to the full bar height — correctly signaling "these are similar." Map the same four values onto a 150–180 axis instead, and the identical value differences now consume the entire available pixel range, so the rendering engine stretches small numeric gaps into large visual ones. The data and the axis labels can both be 100% accurate while the visual impression is completely wrong — the distortion lives entirely in the pixel-to-value mapping, which is exactly why "start bar charts at zero" is a rule about the rendering, not the data.

What a box plot's whiskers and box actually encode. The box spans Q1 to Q3 (the same IQR from Module 04); the line inside is the median, not the mean, so it's robust to the same outliers a mean would be pulled by; the whiskers extend to the most extreme data point still within 1.5×IQR of the box (the identical Tukey rule from Module 04); anything beyond that is drawn as an individual dot. A box plot is, mechanically, the IQR outlier rule and the five-number summary rendered as a picture.

Exercise¶

Using the df from this module, make a scatter plot of age vs. spend and compute their correlation. Then make a bar chart of average age per region. Write one sentence for each chart stating what it shows — and for the bar chart specifically, confirm your y-axis starts at 0.