Mathematics 7–10 · Years 7–8
Hand span of the class: mean, median, mode, range and the effect of one outlier
Statistics and probability
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The idea
A continuous measurement collected from everyone in the room gives a distribution whose centre and spread can be summarised, and one extreme value moves the mean and the range while moving the median by at most half the gap between the two middle values.
What you need
- 30 cm ruler per pair
- Class recording sheet (first names optional; use learner numbers)
- Grid paper for a stem-and-leaf plot and a dot plot
- Calculator or spreadsheet
How to do it
- Define the measurement: hand span is the distance from the tip of the thumb to the tip of the little finger with the hand spread flat on the desk, read to the nearest millimetre. Classify it as continuous numerical data.
- Each learner measures their own span twice and records the mean of the two readings.
- Enter the class values (about 25) on the board; order them and build a stem-and-leaf plot with stems in centimetres and the millimetre digit written to the right of each stem.
- Compute the mean, median, mode (to the nearest 0.5 cm) and range; describe the shape (symmetric, skewed, any gap).
- Add one extra value 10 cm larger than the current maximum and recompute the four statistics; record which ones changed and by how much.
- Compare with the same measurement from a different year group if available.
What you should see
The stem-and-leaf plot shows a single cluster a few centimetres wide. Adding one value 10 cm above the maximum to a class of 25 raises the range by exactly 10 cm and raises the mean by (new value − old mean) ÷ 26; that is more than 10/26 = 0.38 cm, because the new value sits 10 cm above the maximum, not above the mean (with the maximum 2 cm above the mean the rise is 12/26 = 0.46 cm). The median moves from the 13th value to the mean of the 13th and 14th values, a shift of half the gap between them (zero when the two are equal, as often happens with spans recorded to the nearest 0.5 cm), and the mode is unchanged. The learner knows it worked when the recomputed mean rises by exactly (new value − old mean) ÷ 26 while the median moves by no more than half the gap between the 13th and 14th values.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The mean is the best summary in every case.
- The range measures the centre of the data.
- An outlier moves the median as much as it moves the mean.
Safety card
Hazards
No hazard is listed.
Controls
- record learner numbers rather than names on shared sheets
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 4 Data classification and visualisation; page read 2026-09-22MA4-DAT-C-01
- Mathematics K–10 Syllabus (2022), Stage 4 Data analysis; page read 2026-09-22MA4-DAT-C-02
- Australian Curriculum v9AC9M7ST01AC9M7ST02AC9M7ST03
Sources
The pages the author read to write this activity.