Interpreting Plots

It is one thing to make a chart. It is a more advanced skill to read one carefully — to extract everything it is telling you, and to notice everything it is not telling you.

This page is a tour of how to look at a chart. Every analyst needs this, and almost nobody teaches it explicitly.

Step 1: read the axes before the picture

Before you stare at the shape, look at:

• What is on the x axis?
• What is on the y axis?
• What are the units?
• Does either axis start at zero? If not, is that defensible?
• Is either axis on a log scale? (Log axes can make exponential growth look linear and small differences look huge.)

A chart whose y-axis starts at 85 instead of 0 can make a 1% difference look like a mountain. A chart on a log scale can hide a 10× difference. Knowing what scale you're looking at is half the battle.

Step 2: identify the encoding

Every chart maps data to visual properties. Make sure you know the mapping:

• Position (x, y): usually the main variables.
• Color: a third variable.
• Size: sometimes a fourth.
• Shape, line type, panel (facet): more dimensions.

If there's a legend, read it. If a color is encoding something, know what it's encoding before you interpret the picture.

Step 3: look at the shape, then the details

For a scatterplot, ask:

• Direction (positive / negative / no slope)
• Strength (tight band or diffuse cloud)
• Linear or curved?
• Outliers?
• Distinct clusters? (might suggest a hidden category)

For a histogram or density, ask:

• Where's the center?
• How wide?
• Skewed?
• One peak or several?
• Where are the gaps?

For a boxplot, ask:

• Where are the medians?
• Do the boxes (middle 50%) overlap a lot, or are they clearly separate?
• Are the outliers in one direction?
• Are some groups much more variable than others?

For a line chart, ask:

• Trend up, down, flat, or cyclical?
• Sudden changes? Where, and what was happening then?
• Comparable across panels / colors?

Step 4: ask "what isn't shown?"

The most important interpretation question is what's missing from the picture. Some examples:

• A scatterplot of price vs square footage — but what about neighborhood? Bigger houses might cluster in better neighborhoods.
• A line chart of sales over time — but what about inflation? A nominal rise may be a real decline.
• A bar chart of complaints by store — but what about traffic per store? More complaints might just mean more customers.

A chart is a projection — a few dimensions of a higher-dimensional truth. The skilled reader always asks what other dimensions might explain the picture.

Anscombe revisited: four shapes, one summary

We met Anscombe's quartet earlier. Let's actually plot it now, to drive home why looking matters:

All four datasets have almost identical means, standard deviations, correlations, and regression lines. They look nothing alike. Always plot.

A worked example: read this chart

How might you read it?

1. Axes: temperature in °F (x), ozone concentration in parts per billion (y). Both start near the minimum value — not at zero, but that's fine for a scatterplot.
2. Encoding: each dot is one day. No color or facet — just two variables.
3. Shape: clear positive relationship — hotter days have higher ozone. The relationship looks curved: ozone rises slowly at low temps and shoots up at high temps. There's a single far outlier around 90°F.
4. What's missing? Wind, time of day, the day of week, the season, pollution sources. Maybe what we're really seeing is that hot days are usually still days, and ozone accumulates when there's no wind to disperse it. The chart can't tell us that — but we know to ask.

Notice we did not say "high temperature causes high ozone." We said associated with. That's the discipline.

The honest interpretation has hedges

The trained analyst is allergic to overclaiming. Compare:

• ❌ "Temperature drives ozone."
• ✅ "Ozone is positively associated with temperature on hot days in this dataset; further investigation could test whether wind speed accounts for some of the relationship."

This is not just polite throat-clearing. It's accurate. Data shows us associations; causation requires more.

Test your understanding

QuestionSelect one

When reading a chart, what's the very first thing you should look at?

The legend

The axes — their labels, units, scale, and starting values

The colors

The chart's title

QuestionSelect one

Anscombe's quartet shows that:

R sometimes plots data incorrectly.

Correlation is always meaningless.

Datasets with nearly identical summary statistics can have completely different shapes — so you must visualize, not just summarize.

Linear regression is always wrong.

QuestionSelect one

You see a scatterplot showing a positive relationship between ice cream sales and drowning rates. What's the most responsible interpretation?

Ice cream causes drowning.

Drowning causes ice cream sales.

The two are associated; a likely cause is a confounding variable like summer weather, but the chart alone cannot establish causation.

The chart is wrong.

Mini challenge: critique a chart

We've built a deliberately-bad chart of mtcars. Identify the problems by editing the chart into a better one. The starting chart has no title, no axis labels, mapping color to a constant string, and uses pie/3D-style ornamentation we should drop.

We've gone from raw data to summaries to visualizations to interpretation. The next section steps back and asks the deeper question: how can we tell what's real in our data versus what's just noise?