Mathematics 7–10 · Years 9–10
Box plots of reaction time: dominant against non-dominant hand
Statistics and probability
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The idea
A five-number summary and a box plot let two sets of measurements be compared on centre, spread, shape and outliers in one display.
What you need
- 30 cm ruler per pair
- Recording table for 10 catches per hand, converted to seconds with t = sqrt(2d/g), g = 9.8 m/s²
- Grid paper or spreadsheet
How to do it
- Run the ruler-drop procedure for 10 catches with the dominant hand and 10 with the other hand for every learner, converting each catch to a time.
- Pool the class's dominant-hand times and non-dominant times into two data sets.
- For each set order the values and find the minimum, lower quartile, median, upper quartile and maximum; compute the interquartile range.
- Draw the two box plots on one scale; mark any value more than 1.5 interquartile ranges beyond a quartile as an outlier.
- Compare centre, spread and shape in a written conclusion and state whether the medians differ by more than the boxes overlap.
What you should see
As a check of the method, eight catches of 12, 15, 17, 19, 20, 22, 25 and 30 cm convert with t = sqrt(2d/g) to 0.156, 0.175, 0.186, 0.197, 0.202, 0.212, 0.226 and 0.247 s, which have median 0.1995 s, lower quartile 0.1805 s (median of the lower half), upper quartile 0.219 s and interquartile range 0.0385 s, with the outlier fence at 0.219 + 1.5 × 0.0385 = 0.277 s to three decimal places, so the 0.247 s catch is not an outlier. For the class data, how far the two boxes overlap and whether the non-dominant median is higher are what the data answer, and the learner should report the observed difference in medians alongside the interquartile ranges rather than assume a direction. The learner knows it worked when the quartiles hand-computed on a small subset match the spreadsheet's for that subset, and when the box plot's whiskers and box enclose the right counts (about a quarter of the values in each segment).
What changes
- What you change
- hand used
- What you measure
- reaction time
- What you keep the same
- same ruler and procedure
- same number of trials per hand
- order of hands alternated between learners (half start with each hand) so practice does not favour one hand
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The box contains half the values only when the data are symmetric.
- A longer whisker means more data on that side.
- Overlapping boxes mean the medians are equal.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
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 5 Data analysis A; page read 2026-09-22MA5-DAT-C-01
- Australian Curriculum v9AC9M10ST02AC9M9ST03
Sources
The pages the author read to write this activity.