Exercises

Practice choosing, constructing, checking, interpreting, saving, and debugging small plots while keeping the underlying numbers visible.

These exercises combine plot choice, construction, interpretation, fair comparison, saving, and visual debugging. Check the numbers beside the figure instead of judging the image alone.

Q1. Choose a view for ordered readings

You recorded one temperature every hour. Which plot best preserves the order and spacing of the measurements?

Choose one

A line plot with a marker at each recorded hour

A bar plot after sorting the temperatures

A histogram with the hours removed

Select one choice, then check.

HintIdentify the relationship

The question asks how one value changes across ordered time.

SolutionKeep time on the horizontal axis

Use a line plot with hour on the horizontal axis and temperature on the vertical axis. Markers distinguish recorded values from connecting segments.

Q2. Calculate one bar height

The valid reading counts for sensors A and B are 3 and 2. What height should the bar for sensor B have?

Bar height

Compute it first, then check your number.

HintKeep each name with its value

Sensor B is paired with the second count.

SolutionUse the category magnitude

The bar for sensor B has height 2 and normally begins at zero.

Q3. Preserve measurement pairs

Why is it wrong to sort sensor_a without applying the same order to sensor_b before drawing a scatter plot?

Choose one

Matching positions may no longer describe the same observation.

Scatter plots require both arrays to be increasing.

Sorting changes the number of values.

Select one choice, then check.

HintTrace one point

Point i is formed from sensor_a[i] and sensor_b[i].

SolutionKeep row identity

Sorting only one array changes which two values form a point, so the plot no longer represents the observed pairs.

Q4. Count a histogram bin

Using edges [0, 2, 4, 6], how many values in [0.5, 1.5, 2.0, 3.5, 5.0] fall in the first interval from 0 up to, but not including, 2?

Count

Compute it first, then check your number.

HintCheck each value against both edges

The value 2.0 begins the next interval.

SolutionCount the first interval

Only 0.5 and 1.5 satisfy

0 \le x < 2

, so the count is 2.

Q5. Display a centered table fairly

Complete the heatmap so zero is the midpoint and values -2 and 2 use equal color limits.

Editable Python

HintMake zero the reference

Pass cmap="coolwarm", vmin=-2, vmax=2 to imshow.

SolutionUse symmetric diverging limits

image = ax.imshow(centered, cmap="coolwarm", vmin=-2, vmax=2) maps equal positive and negative magnitudes consistently.

Q6. Separate evidence from explanation

Which sentence is an observation supported directly by a line plot?

Choose one

The final plotted reading is lower than the preceding reading.

The sensor fell because its battery is failing.

Every future reading will continue to fall.

Select one choice, then check.

HintDescribe before explaining

Use only positions visible in the plot.

SolutionState the visible comparison

The plot supports that the final point is below the preceding point. Battery failure and future behavior require more evidence.

Q7. Find a misleading bar axis

A bar plot compares values 98 and 100, but its vertical axis begins at 97. What is the main risk?

Choose one

The visible bar lengths exaggerate a difference of only two units.

The category names can no longer be displayed.

Matplotlib changes the stored values to 1 and 3.

Select one choice, then check.

HintRemember what bar length encodes

Bars are usually judged from their baseline.

SolutionKeep magnitude comparison honest

Starting near 97 makes 98 and 100 look far more different than their values are. A zero baseline is the usual honest choice for magnitude bars.

Q8. Use shared histogram edges

Two groups must be compared by histogram. Which construction permits a fair bin-by-bin comparison?

Choose one

Choose one explicit edge array and pass it to both histograms.

Let each group choose unrelated automatic bins.

Sort both groups and connect the values with lines.

Select one choice, then check.

HintMatch interval boundaries

A bar can be compared only with a bar covering the same numerical range.

SolutionReuse explicit bins

Define one edge array, such as bins = np.array([-2, -1, 0, 1, 2]), and use bins=bins for both datasets.

Q9. Save and close the intended figure

Complete the final two operations for a figure named fig.

Editable Python

HintKeep figure ownership explicit

Call fig.savefig(path, ...), then plt.close(fig).

SolutionSave and release one figure

Use fig.savefig(path, dpi=150, bbox_inches="tight") followed by plt.close(fig).

Q10. Check a heatmap orientation

For table[2, 1] == 18, which displayed position should carry the value 18 when imshow(table) is used without transposing it?

Choose one

Row 2, column 1

Row 1, column 2

Position 18 on a one-dimensional axis

Select one choice, then check.

HintRead both indices in order

NumPy indexing is table[row, column].

SolutionMap array axes directly

The value appears at displayed row 2, column 1. Checking this known cell helps detect an accidental transpose.

Q11. Locate a wrong computed point

The reference is [2, 3, 4] and the computed result is [2, 7, 4]. What is the index of the first disagreement?

Index

Compute it first, then check your number.

HintCompare in order

Index zero agrees. Inspect the next pair.

SolutionFind the first divergence

The first mismatch is at index 1. That small location should be tested before changing the complete program.

Q12. Verify a visual repair numerically

Complete the check after repairing one wrong transformed value.

Editable Python

HintCheck the complete result

Set verified from np.allclose(computed, reference).

SolutionKeep numerical evidence beside the plot

verified = np.allclose(computed, reference) returns True only when all repaired values agree within tolerance.

You can now choose the smallest plot that preserves the needed relationship, check its construction against the numbers, describe its evidence carefully, and use it with numerical tests to find a wrong result. Chapter 13 adds controlled random variation to these deterministic computations.

Q1. Choose a view for ordered readings

Q2. Calculate one bar height

Q3. Preserve measurement pairs

Q4. Count a histogram bin

Q5. Display a centered table fairly

Editable Python

Q6. Separate evidence from explanation

Q7. Find a misleading bar axis

Q8. Use shared histogram edges

Q9. Save and close the intended figure

Editable Python

Q10. Check a heatmap orientation

Q11. Locate a wrong computed point

Q12. Verify a visual repair numerically

Editable Python

Pause and reflect