Case A
Stated target: 50- 48
- 49
- 50
- 51
- 85
Mean = __________ ; error = __________Median = __________ ; error = __________
The smaller error belongs to: ____________________
Check Case A interactively ↗Free classroom activity / three cases
Can the mean lose, win, and tie?
Make three predictions, show the arithmetic, then explain why one estimator cannot win every case. Each digital check hides its answer until you choose.
Download print-ready PDF ↓Start the student sheet ↓
The PDF has a designed student page and a separate worked answer key. Print page 1 for student copies; keep page 2 for discussion.
Student sheet
Which estimate is closer to the stated target?
NameDate
For each invented set of five readings, predict first. Then calculate the mean (sum ÷ 5), the median (middle value after sorting), and each absolute error (distance from the stated target). Choose the smaller error, or equal error if they tie.
Case B
Stated target: 52- 40
- 42
- 50
- 60
- 68
Mean = __________ ; error = __________Median = __________ ; error = __________
The smaller error belongs to: ____________________
Check Case B interactively ↗Case C
Stated target: 50- 0
- 0
- 50
- 100
- 100
Mean = __________ ; error = __________Median = __________ ; error = __________
The smaller error belongs to: ____________________
Check Case C interactively ↗Explain: What do these three cases show about claiming that the mean or median is always closer?
Teacher answer key and discussion
Worked answer key
| Case | Mean / error | Median / error | Closer |
|---|---|---|---|
| A | 283 ÷ 5 = 56.6 / 6.6 | 50 / 0 | Median |
| B | 260 ÷ 5 = 52 / 0 | 50 / 2 | Mean |
| C | 250 ÷ 5 = 50 / 0 | 50 / 0 | Equal error |
Discussion: The winner depends on both the readings and the reference target. A high reading does not automatically make the median closer; Case B is a counterexample. A tie is possible even with readings at both ends of the scale.
To change only the reference while holding the readings fixed, explore Case A in Target Lens ↗.
To change one reading while holding the reference fixed, find Case A's flip points ↗.
The targets are chosen for these invented exercises. They are not independently measured truths. In real data, a trustworthy target may be unknown; an unusual observation is not automatically invalid.
Use the five-minute lesson ↗ · Change the numbers in the lab ↗
Digital worksheet and blind case checks: aruintelligence.github.io/inward-mathematics-simulator/worksheet.html. The interactive challenge links include the five invented values and target in the URL.