Choosing a Plot

Choose a plot from the numerical question and the structure needed to answer it. Line plots preserve order, scatter plots preserve pairs, histograms preserve value counts, and array or surface displays preserve spatial coordinates.

A numerical array contains values and structure. Before choosing a plot, decide which part of that structure matters:

• the order of the values;
• the pairing between two quantities;
• the distribution of one quantity;
• the rows and columns of a two-dimensional array;
• the output of a function across two input axes.

Different plots preserve different structure. A line plot preserves order. A scatter plot preserves pairs without connecting them. A histogram keeps value counts but discards order. The first question is therefore not “Which Matplotlib function should I call?” It is “What do I need to inspect?”

Begin with a numerical question

Suppose a training program records one loss value after each epoch:

The question “Does loss decrease as training proceeds?” depends on epoch order. A line plot keeps that order and connects consecutive observations.

Now suppose a model produces one prediction for each target:

The question “Are predictions close to their targets?” depends on paired values, not on which example happened to be stored first. A scatter plot keeps each target–prediction pair without suggesting a sequence.

The data alone does not determine the plot. The question and the meaning of the axes determine it.

Preserve the structure you need

This table provides a starting point:

These are not automatic rules. A one-dimensional array can be shown as a line plot or a histogram, but the two plots answer different questions. The line plot keeps the array's order. The histogram discards that order and summarizes how often values occur within intervals.

Compare three views of related data

Run this example and inspect the meaning of each panel. You can edit the measurements or change the number of histogram bins.

The first panel shows when the training loss changes. The second treats each training and validation loss as one pair. The third shows how validation-loss values are distributed, but it no longer shows which epoch produced each value.

Inspect numbers and plots together

A plot summarizes numerical values through position, length, color, or area. That summary can reveal patterns quickly, but it can also hide exact values. Keep small numerical checks beside the figure:

These checks answer questions that the plot may not answer precisely. They can also expose a wrong shape, an unexpected range, or a missing value before you interpret the image.

The reverse is also true: a printed mean can look reasonable while a plot reveals two clusters or one unusual point. Numerical summaries and plots support each other.

Check the axes before the pattern

Before interpreting a plot, identify:

1. what quantity each axis contains;
2. what one point, line, bar, or cell represents;
3. whether order and pairing have been preserved;
4. whether the axes are linear or logarithmic;
5. whether limits or color scales hide part of the data.

A curve can appear steep because the vertical range is narrow. Two heatmaps can use the same color for different values if they have different color limits. A scatter plot can lose its relationship if one array was shuffled without the other. Read the plot's construction as carefully as its visible pattern.

Separate observation from explanation

Begin with a statement that another reader can verify from the figure:

The validation loss decreases through epoch 4, then increases at epoch 5.

This is an observation. It describes visible evidence.

Then propose an explanation:

The increase may indicate that the model has started to fit the training data
more closely without improving on validation data.

This is an interpretation, not a fact established by the plot. It suggests what to investigate next. Keeping these two statements separate prevents a plausible story from being mistaken for evidence.

Plot small results early

A small plot can check a computation before it becomes part of a larger experiment. For example, plot six points from a formula before evaluating it at a million positions. If the small curve has the wrong direction or shape, inspect the formula while every value is still easy to calculate by hand.

Plotting early does not replace tests or shape checks. It adds another form of evidence:

question -> small computation -> numerical checks -> plot -> observation

Use that sequence throughout the chapter.

Retain the question–structure–plot method

For each new figure:

1. write the numerical question;
2. name the structure that the answer depends on;
3. choose a plot that preserves that structure;
4. keep useful numerical checks;
5. state the visible observation before proposing an explanation.

The following lessons apply this method to each plot type in more detail.