Learn

Learning preferences

Make learning more comfortable. Changes apply immediately.

Enlarges page content, including diagrams and their labels. You can also use your browser’s zoom.

Choose the colours that are easiest for you to distinguish. Applies to lesson diagrams and lab plots. Labels, shapes, hatching and line patterns also distinguish meanings. Source photographs and raw image brightness stay unchanged; mask-only views are available for image overlays.

ExampleComparisonSample link

Saved in this browser on this device. Preferences are separate from progress backups.

Learn through experiments

Audit a dramatic chart

Did the data change, or just the visible baseline?

Entering midway? Revisit Which average tells the story? for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Two synthetic dashboard scores are shown as bar heights relative to a controllable lower axis bound. The numerical measurements remain visible.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict whether raising the baseline changes the actual percentage increase.

3 · Experiment

Change one thing. Inspect what happens.

  1. At scores 60 and 66, compute the actual change and relative change.
  2. Raise the lower bound to 30; compare visible-height ratio with the true ratio.
  3. Reverse the two measurements. Write an honest title with units and denominator.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
A measurement60 points
B measurement66 points
Actual change6 points
Actual relative change10 %
Visible height ratio B/A1.1

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
066
  • A visible height (% of plot; selected baseline)60
    A visible height (% of plot; selected baseline): 60Horizontal bar from zero to 60, on the shared zero to 66 numeric axis.
  • B visible height (% of plot; selected baseline)66
    B visible height (% of plot; selected baseline): 66Horizontal bar from zero to 66, on the shared zero to 66 numeric axis.

Follow the calculation

  1. Fixed upper axis bound 100; selected lower bound 0.
  2. A height = (60 − 0)/(100 − 0) = 60% of plot height.
  3. B height = (66 − 0)/(100 − 0) = 66%.
  4. Actual relative change = (66 − 60)/60 × 100 = 10%.

Changing the axis changes visible heights, not measurements. Bar-height ratios require a zero baseline; a clearly labeled point plot can show a narrow range.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

Audit a dramatic chart

Two synthetic dashboard scores are shown as bar heights relative to a controllable lower axis bound. The numerical measurements remain visible.

Predict before changing inputs

Predict whether raising the baseline changes the actual percentage increase.

Understand the mechanism

A change of 6 points on a baseline of 60 is 10%, because 6/60 = 0.10. Percentage points and relative percentages answer different questions.

At lower axis 30 and upper 100, visible heights are 30/70 and 36/70. Their ratio is 1.2 even though measurement ratio is 1.1.

Bars encode magnitude by length. Their baseline matters; use zero for magnitude comparisons or choose a clearly labeled point chart for local differences.

Calculate it yourself

Visible height = (measurement − axis minimum)/(axis maximum − axis minimum). Relative change = (B − A)/A.

Guided investigation

  1. At scores 60 and 66, compute the actual change and relative change.

  2. Raise the lower bound to 30; compare visible-height ratio with the true ratio.

  3. Reverse the two measurements. Write an honest title with units and denominator.

Assumptions and limitations

  • Scores are invented, and the chart models geometry rather than a real dashboard.

  • An honest axis does not fix unrepresentative data or an inappropriate metric.

Further investigations

High school: Redraw one fictional claim with a zero baseline and explicit units.

College: Compare bar and point encodings for the same measurements.

Working professionals: Create a dashboard review checklist covering units, baselines, denominators and missing data.

5 · Apply

Try a fresh case

A metric rises from 80 to 88. What is its relative percentage increase?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Redraw one fictional claim with a zero baseline and explicit units.

College investigation

Compare bar and point encodings for the same measurements.

Workplace investigation

Create a dashboard review checklist covering units, baselines, denominators and missing data.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.