Mathematics 11–12 · Year 11
Reaction times from the ruler drop: a class dataset for centre, spread and outliers
Data analysis: Measures of centre and spread (Mathematics Standard, Year 11); Data analysis: Clusters and outliers (Mathematics Standard, Year 11); Probability and data: Data (Mathematics Advanced, Year 11: the frequency table, histograms, median and mode only; the standard deviation, quartiles and outlier test are Mathematics Standard content)
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The idea
A variable measured by every learner becomes a real distribution whose mean, median, standard deviation, quartiles and outliers mean something because the learners produced it.
What you need
- One 30 cm ruler per pair
- A table edge, a recording sheet, a spreadsheet
- The conversion t = sqrt(2d / g) with g = 9.80 m/s^2 (the Science World reaction-time ruler uses the same free-fall relation)
How to do it
- Partner A holds the ruler vertically with the 0 cm mark level with the top of partner B's open thumb and finger; B rests the forearm on the table edge.
- A drops the ruler without warning at a random moment within 5 s; B catches it and reads the distance d at the top of the thumb. Five catches each; the first is practice and is discarded.
- Convert each d to a time with t = sqrt(2d / g) and record the median of the four kept catches as that learner's reaction time; record a miss as a miss, not as 30 cm.
- Pool the class values (no names needed); build a frequency table, a histogram and a box plot; compute the mean, median, mode, range, population standard deviation and IQR.
- Test each value against Q1 - 1.5 IQR and Q3 + 1.5 IQR and discuss any outlier and its effect on the mean and the median.
- Repeat with the non-dominant hand as a second dataset and compare the two box plots.
What you should see
Catches at 10, 15, 20, 25 and 30 cm convert to 0.143, 0.175, 0.202, 0.226 and 0.247 s, so every catch on a 30 cm ruler lies between 0 and 0.247 s and the distance is not proportional to the time. For the model's test catches of 12, 14, 15, 16, 17, 18 and 29 cm the times are 0.156, 0.169, 0.175, 0.181, 0.186, 0.192 and 0.243 s; the median is 0.181 s, Q1 = 0.169 s, Q3 = 0.192 s, IQR = 0.023 s, and the upper fence of 0.226 s flags the 29 cm catch (0.243 s) as an outlier; removing it lowers the mean from 0.186 s to 0.177 s but moves the median only from 0.181 to 0.178 s. The learner knows it worked when each person's four catches cluster within a few centimetres and the class histogram has a single peak.
What changes
- What you change
- hand used (dominant or not)
- What you measure
- reaction time
- What you keep the same
- ruler held at 0 cm level with the fingers
- same warning-free drop protocol
- forearm resting on the table
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The catch distance is the reaction time; distance grows with the square of time, so 20 cm is not twice as slow as 10 cm.
- An outlier is any value far from the mean; the Mathematics Standard syllabus test uses the quartile fences.
- The mean is always the best summary; one slow catch moves the mean far more than the median.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No chemicals and no 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 Standard 11–12 Syllabus (2024), Year 11 focus area Data analysis; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-11-08
- Mathematics Advanced 11–12 Syllabus (2024), Year 11 focus area Probability and data; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-11-10
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.