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Learn through experiments

Which average tells the story?

What changes when the slowest service disappears from the log?

Entering midway? Revisit Repair a messy event log for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Five original synthetic service waits start at 10, 12, 14, 16 and a controllable final value, in minutes. Inspect the mean, median and missingness.

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 which summary moves most when one wait becomes very long.

3 · Experiment

Change one thing. Inspect what happens.

  1. Record all waits. Change the fifth wait from 20 to 100 and compare mean with median.
  2. At 100 minutes, omit the longest wait. Did service improve or only the record?
  3. Move the fifth wait to 10. Read the sorted trace before predicting the median.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Recorded mean22.4 minutes
Recorded median14 minutes
Recorded count5

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.
060
  • Recorded wait 1 (minutes)10
    Recorded wait 1 (minutes): 10Horizontal bar from zero to 10, on the shared zero to 60 numeric axis.
  • Recorded wait 2 (minutes)12
    Recorded wait 2 (minutes): 12Horizontal bar from zero to 12, on the shared zero to 60 numeric axis.
  • Recorded wait 3 (minutes)14
    Recorded wait 3 (minutes): 14Horizontal bar from zero to 14, on the shared zero to 60 numeric axis.
  • Recorded wait 4 (minutes)16
    Recorded wait 4 (minutes): 16Horizontal bar from zero to 16, on the shared zero to 60 numeric axis.
  • Recorded wait 5 (minutes)60
    Recorded wait 5 (minutes): 60Horizontal bar from zero to 60, on the shared zero to 60 numeric axis.

Follow the calculation

  1. Original synthetic waits, sorted: 10, 12, 14, 16, 60 minutes.
  2. All five waits are recorded.
  3. Sum = 10 + 12 + 14 + 16 + 60 = 112; mean = 112/5 = 22.4.
  4. Middle of the sorted record = 14 minutes.

The median describes a typical recorded wait; the mean captures total recorded waiting burden per person. Neither repairs missing observations.

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

Which average tells the story?

Five original synthetic service waits start at 10, 12, 14, 16 and a controllable final value, in minutes. Inspect the mean, median and missingness.

Before you change anything

Predict which summary moves most when one wait becomes very long.

Follow the mechanism

The mean divides total waiting minutes by people. The median is the middle sorted wait, or the average of the two middle waits for an even count.

At 10, 12, 14, 16, 60 the mean is 112/5 = 22.4 minutes and the median is 14. Both are correct answers to different questions.

Deleting a long wait changes the dataset. A lower displayed average is not evidence of faster service.

Calculate it yourself

Mean = sum of recorded waits ÷ recorded count; median = middle sorted value(s).

Try a counterexample

  1. Record all waits. Change the fifth wait from 20 to 100 and compare mean with median.

  2. At 100 minutes, omit the longest wait. Did service improve or only the record?

  3. Move the fifth wait to 10. Read the sorted trace before predicting the median.

What this model leaves out

  • Five invented observations cannot establish the usual performance of a real service.

  • Missing values are deliberately selective here. Real missingness requires investigation.

Take it further

High school: Compare mean and median for anonymized classroom travel times.

College: Study trimmed means and how missingness changes an estimator.

Working professionals: Propose a service dashboard with counts, tail waits and explicit missing-data rates.

5 · Apply

Try a fresh case

Fresh waits are 2, 4, 6 and 20 minutes. What is their median in minutes?

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

Compare mean and median for anonymized classroom travel times.

College investigation

Study trimmed means and how missingness changes an estimator.

Workplace investigation

Propose a service dashboard with counts, tail waits and explicit missing-data rates.

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.