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Data, probability and statistics I · Lesson 05 / 12

What the center hides

Two routes average four minutes. One is consistent; the other varies considerably. That difference matters when planning a delivery.

Learning paths16 min

Let's discover together

  1. 1

    Load Same mean: A = 4, 4, 4, 4; B = 1, 3, 5, 7. Each sums to 16 across four records: both have mean 4 and median 4. The lists are nevertheless different.

  2. 2

    Range is maximum minus minimum. For A: 4 − 4 = 0 minutes; for B: 7 − 1 = 6 minutes. Range uses only two extremes and does not reveal how the other values are distributed.

  3. 3

    Inspect each observation in the table and bars. For a five-minute deadline, all four A deliveries met it; three of four B deliveries did. The mean alone does not answer that question.

  4. 4

    A smaller range in these records does not prove the route will always be consistent. More observations may reveal other extremes. This introduction uses range and individual values; variance, standard deviation and intervals belong to later study.

Evidence lab

Experiment with fictional deliveries at Aurora station. Analysis runs in this browser. Nothing entered here is sent to the server.

The workshop resets when you leave or reload. Download data and report to keep your work, or send the report to the activity editor, which keeps a draft in this browser. Completion and XP belong to the account.

Header id,group,minutes; one delivery per row; unique id; groups A/B; decimal point; duration 0–1440 with up to two decimal places. Blank means unknown. Up to 100 rows. No quotes or decimal commas. Use invented data.

Selection uses the entered table, including missing values. A draw does not guarantee representativeness. The same seed reproduces selection; it cannot recover cases outside the table.

Make a prediction and analyze the table.

Virtual bag: model with replacement

There are four equally likely tokens; choose how many are blue. Each token returns before the next draw. This is a deterministic simulation, without prizes, money or real observations.

Repeating the seed repeats the sequence. More draws do not guarantee a closer result in every run and do not validate the real-world model.

Two rules, the same accuracy

Ten fictional cases: nine normal and one failure. Rules defined for this example; no AI training or real equipment testing. Same number correct, different consequences.

Two rules, the same accuracy
RuleCorrect / totalMissed failuresFalse alarms

Your investigation report

Official links and next step

✦
YOUR MISSION

Compare distributions using center, extremes and range.

Now it's your turn

Discovery workshop

Predict, check, explain

Compare distributions using center, extremes and range.
Build your answers and check when you are ready.
A moment to understand

Does having the same mean guarantee the same consistency?

I need a hint

Center and spread answer different questions. Report the cases, sample size and comparison limits.

Loading your journey…

Take it with you

Build two lists with equal means and different ranges. Then create lists with the same range but different internal values. Explain what each summary failed to show.

At your own pace

My files and GitHub

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