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Data, probability and statistics I · Lesson 04 / 12

Mean and median tell different stories

In the Extreme value example, four deliveries were short and one took 24 minutes. One number can hide this difference.

Learning paths18 min

Let's discover together

  1. 1

    Order 2, 4, 4, 6, 24. The sum is 40 across five values: mean = 40/5 = 8 minutes. The median is the middle value of the sorted list: 4. It is not the id of the spreadsheet’s middle row.

  2. 2

    With an even count, average the two middle values. For 2, 4, 6, 8, the median is (4 + 6)/2 = 5. Sorting is essential; the mean does not depend on row order.

  3. 3

    Replace 24 with 40 in the workshop and predict the effect. The mean becomes 11.2; the median stays 4. That does not make 24 an error: it could be important. Investigate before excluding it.

  4. 4

    The mean divides a total; the median describes a center by position. State the question and examine the distribution. Averaging two means directly gives the combined mean only when the groups have equal sizes.

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

Calculate mean and median and explain why neither replaces the other.

Now it's your turn

Discovery workshop

Predict, check, explain

Calculate mean and median and explain why neither replaces the other.
Build your answers and check when you are ready.
A moment to understand

Why can mean 8 and median 4 both be correct?

I need a hint

A measure of center does not describe every case. Do not choose a measure merely because it favors your conclusion.

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Take it with you

Create five durations with median 6 and one much larger duration. Calculate mean and median by hand, check them and explain which question each helps answer.

At your own pace

My files and GitHub

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