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Learn through experiments

Repair the survey headline

Which people does a percentage actually describe?

Entering midway? Revisit Repair an unclear instruction for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Original fictional survey: invitees may respond, and respondents may report satisfaction. Nonresponse is unknown. Sliders retain requested counts. The model caps actual responses at invitations and actual satisfied respondents at actual responses; metrics, bars and traces use those actual counts.

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 satisfaction among respondents stays fixed when you add unanswered invitations.

3 · Experiment

Change one thing. Inspect what happens.

  1. Calculate the initial respondent percentage before reading the trace.
  2. Change invitations only; explain which percentage changes.
  3. Reduce responses below the satisfied count and inspect the capped counts.
  4. Write a headline and one sentence describing missing evidence.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Actual respondents after caps80 people
Satisfied among respondents75 %
Known satisfied among invited30 %

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.
0120
  • Satisfied respondents60
    Satisfied respondents: 60Horizontal bar from zero to 60, on the shared zero to 120 numeric axis.
  • Other respondents20
    Other respondents: 20Horizontal bar from zero to 20, on the shared zero to 120 numeric axis.
  • No response120
    No response: 120Horizontal bar from zero to 120, on the shared zero to 120 numeric axis.

Follow the calculation

  1. Requested 80 responses and 60 satisfied respondents. Actual counts after caps: invited 200, responses 80, satisfied 60.
  2. Among respondents: 60/80 × 100 = 75.0%.
  3. Known satisfied among invited: 60/200 × 100 = 30.0%.
  4. Unanswered invitations are unknown, not dissatisfied. Counts are capped so satisfied ≤ responses ≤ invited.

A defensible sentence names the denominator: “60 of 80 respondents reported satisfaction.” It cannot establish satisfaction among all invitees.

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

Repair the survey headline

Original fictional survey: invitees may respond, and respondents may report satisfaction. Nonresponse is unknown. Sliders retain requested counts. The model caps actual responses at invitations and actual satisfied respondents at actual responses; metrics, bars and traces use those actual counts.

Follow the mechanism

A percentage is a part divided by a named whole. The same 60 satisfied people are 75% of 80 respondents but 30% of 200 invitees.

Calling 30% the satisfaction rate of all invitees treats unknown answers incorrectly. It is the known satisfied fraction only.

An empty respondent group has no satisfaction rate; the result is displayed as Undefined.

Worked example

Requested 80 responses and 60 satisfied respondents. Actual counts after caps: invited 200, responses 80, satisfied 60.

Among respondents: 60/80 × 100 = 75.0%.

Known satisfied among invited: 60/200 × 100 = 30.0%.

Unanswered invitations are unknown, not dissatisfied. Counts are capped so satisfied ≤ responses ≤ invited.

Calculation

Respondent satisfaction = satisfied ÷ responses × 100; known satisfied fraction = satisfied ÷ invited × 100.

Try a controlled comparison

  1. Calculate the initial respondent percentage before reading the trace.

  2. Change invitations only; explain which percentage changes.

  3. Reduce responses below the satisfied count and inspect the capped counts.

  4. Write a headline and one sentence describing missing evidence.

What this does not establish

  • No text scoring is performed; a correct calculation cannot certify clear or responsible writing.

  • Survey wording, sampling and honesty are not modeled.

5 · Apply

Try a fresh case

Of 240 invitees, 90 respond and 54 report satisfaction. What percentage of respondents report satisfaction?

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

Rewrite three fictional percentage claims with explicit denominators.

College investigation

Write a survey results paragraph with uncertainty and recruitment limitations.

Workplace investigation

Audit a fictional dashboard summary for missing denominators and unsupported generalization.

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.