Choose and Interpret a Plot
Choose a plot from the question and the relationship it must preserve, then state what the visible evidence shows before proposing an explanation.
We have used five plot forms, each for a different relationship. Choosing among them begins with the question: which structure must remain visible? The number of values or the shape of an array does not decide the plot by itself.
Match the Question to the Preserved Structure
Use the smallest view that keeps the relationship needed by the question:
| Question | Structure that must remain visible | Useful first plot |
|---|---|---|
| How does a reading change across ordered observations? | order | line |
| How do named sensor means compare? | category name and magnitude | bar |
| How do two measurements vary as pairs? | one matched pair per observation | scatter |
| Where do residual values concentrate? | counts within numerical intervals | histogram |
| Where do values sit in an observation-by-sensor table? | two-dimensional positions and values | heatmap |
These are choices from a question, not names to memorize. The same one-dimensional residual array could appear in a line plot if observation order matters or in a histogram if concentration and spread matter. The plots answer different questions because one keeps order and the other discards it.
Q1. Choose a plot for ordered readings
We need to see whether one sensor's reading rises or falls from observation 0 through observation 5. Which first plot preserves the required relationship?
Select one choice, then check.
HintKeep the sequence
The question contains “from observation 0 through observation 5.” The plot must retain that order.
SolutionUse a line plot
Put observation order on the horizontal axis and the reading on the vertical axis. A histogram would discard the order the question needs.
Inspect the Numbers beside the Plot
A plot makes relationships visible but does not replace the array. Before interpreting a figure, print or calculate small checks that establish its data contract:
For paired data, also check that both arrays have the same length and that their order still matches. For a histogram, verify the bin edges and total count. For a heatmap, inspect its shape, axis meanings, and one known cell.
The executable example below places the five questions beside five views of the recurring measurement data. The printed evidence remains small enough to check before looking at the panels.
Compare five questions and five views
Each panel preserves a different relationship. Inspect the printed values first, then identify what each plot keeps and discards.
Ready to run.
One panel should not be used to make every claim. The line plot shows that sensor 0 rises across the three ordered observations. It does not show the residual distribution. The histogram shows that most residuals lie near zero, but it cannot say when any residual occurred. The heatmap preserves both table axes, but a three-value line is clearer for the simple order question.
Q2. Choose a plot for paired measurements
Each row contains one sensor-0 reading and the sensor-1 reading recorded at the same observation. We want to inspect how the two readings vary together. Which plot should we begin with, and what must the program preserve?
Select one choice, then check.
HintKeep row identity
The two arrays must have equal lengths and matching order so point i uses
both values from observation i.
SolutionUse a scatter plot without breaking pairs
Plot sensor 0 on one axis and sensor 1 on the other, keeping their shared observation order. Separate histograms would discard the pairing.
State an Observation before an Explanation
Begin interpretation with a claim another reader can verify directly from the numbers or figure:
The sensor-0 readings rise from 2 to 4 across observations 0 to 2.
That is an observation. It describes visible evidence. A sentence such as “the room warmed because sunlight entered” is an explanation. It may be a reasonable hypothesis, but these three readings do not establish the cause.
Before stating either, check the construction:
- axes and units;
- preserved order, categories, or pairs;
- baseline, bin edges, or color limits;
- underlying shape, range, and selected values.
A clear plot can still support a false interpretation if a pair was broken, an axis was truncated, bins differed between panels, or a table was transposed.
Q3. Separate observation from explanation
Which sentence is a direct observation supported by the fixed histogram
counts [1, 4, 5, 1, 1]?
Select one choice, then check.
HintReport evidence before cause
The counts can establish where these twelve values fell. They cannot identify a faulty sensor or predict every future sample.
SolutionDescribe the visible counts
The two bins nearest zero have counts 4 and 5, while each other bin has
count 1. This is a direct description of the fixed sample.
Choose a plot from the relationship the question must preserve: order, names, pairs, a one-value distribution, or a two-dimensional table. Inspect the underlying numbers and construction, then state a visible observation before proposing an explanation. The next lesson makes figures comparable and saves their context for later inspection.