Histograms

A histogram answers a single, fundamental question: what does the distribution of this one variable look like? Where do most values cluster? Is the distribution symmetric or skewed? Are there outliers? Is it bell-shaped, uniform, or bimodal?

You will use histograms constantly during exploratory analysis — every time you load a new dataset, you should histogram every numeric column as part of getting acquainted.

How a histogram works

A histogram chops the range of a numeric variable into bins (usually equal-width buckets) and shows the count of values that fall into each bin. The result looks like a bar chart, but the bars represent intervals, not categories.

The simplest histogram

You can see immediately: most bills are between $10-25, the distribution has a *right tail* (a few large bills), and very few bills exceed$40.

Bin width matters — a lot

The number of bins you choose changes how the distribution looks. Too few bins hide structure; too many bins create noise.

Edit the code: try nbins=5, then 100. You'll see two failure modes — too-few hides the shape; too-many turns the chart into noise.

A useful default heuristic is the square-root rule: number of bins ≈ √n, where n is the row count. For tips() (244 rows), √244 is about 16, which is a reasonable starting point. Plotly's own default is sensible for most datasets; only override when you have a reason.

Comparing groups: stacked, grouped, or overlaid

Add color="..." to split the histogram by a categorical variable:

barmode="overlay" with reduced opacity lets two distributions sit on top of each other so you can compare their shapes. Other options:

• barmode="stack" — stacks the counts (good for showing composition, bad for comparing distributions).
• barmode="group" — places bars side by side per bin (can get noisy fast).

Histograms of proportions with histnorm

If your groups have very different sizes, counts are misleading — the larger group will always have taller bars. Use histnorm to normalize:

Now the bars represent probability density (so each group's total area sums to 1), making the shapes directly comparable regardless of group size.

Other histnorm values: "percent", "probability", "density".

When NOT to use a histogram

• For categorical data, use a bar chart (px.bar) showing counts per category, not a histogram.
• For comparing summary statistics across many groups, a box plot (next page) is more concise.
• For two numeric variables, use a 2-D density heatmap or scatter plot.

A real-world reading of a histogram

When you look at a histogram, ask:

1. Where is the center? (Mode, median, mean.)
2. How spread out is it? (Standard deviation, IQR.)
3. Is it symmetric or skewed? Most real-world distributions (income, wait times, page views) are right-skewed — a long tail of large values.
4. Are there multiple peaks (bimodality)? This often signals two mixed populations, which is a big analytical clue.
5. Are there outliers / extreme values?

Train yourself to ask these five questions on every histogram you ever see.

Check your understanding

QuestionSelect one

What is a histogram designed to show?

The relationship between two variables.

A comparison across distinct categories.

The distribution (shape, spread, center, skew) of a single numeric variable.

A trend over time.

QuestionSelect one

What happens if you choose too few bins for a histogram?

The chart looks noisy.

The chart fails to render.

Structure in the distribution (e.g., bimodality, fine clustering) gets averaged away — you only see a coarse outline.

QuestionSelect one

You're comparing the bill-size distribution between two groups with very different group sizes. Why might raw counts on a histogram be misleading?

Raw counts are illegal.

Raw counts force a log scale.

The larger group will always have taller bars, even if the shape of the distributions is similar — counts confound group size with distribution shape.

Raw counts are always wrong.

QuestionSelect one

Which of the following is a sign of a bimodal distribution on a histogram?

A single tall peak in the middle.

A long tail on the right side.

Two distinct peaks separated by a valley.

All bars at the same height.

QuestionSelect one

Which question would a histogram NOT help answer?

"What's the most common range of values?"

"Are there outliers far from the typical range?"

"What's the correlation between income and education?"