Pencils are useful for writing, erasing, and drawing. They are also cheap, light, and aerodynamic projectiles, and it is not uncommon for people to launch one off a desk or any flat surface with a flick of the hand. As a pencil-launching enthusiast (at the time of this study), I set out to settle the matter scientifically: do graphite pencils or mechanical pencils fly farther?
The experiment
I ran a proper randomized, controlled experiment for my freshman year Research Statistics course:
- Independent variable: 60 pencils — 30 graphite, 30 mechanical — launched in a randomized order generated in R.
- Response variable: distance flown, in inches, from launch point to pencil tip.
- Method: a purpose-built Pencil-Launching Apparatus (books, a roller, and a tape measure secured under the table) to deliver a repeatable launch with a fixed 2.5 in. of pencil suspended over the edge.
Results
Graphite pencils won, and not by a little:
| Graphite | Mechanical | |
|---|---|---|
| Mean distance | 33.06 in | 26.27 in |
| Std. deviation | 10.40 in | 8.31 in |
| Sample size | 30 | 30 |
A two-sample t-test gave t = 2.79, p = 0.0036, well below α = 0.05, so the difference is statistically significant. Mechanical pencils flew about 13% shorter on average, likely because their eraser end makes the weight distribution less uniform, increasing air resistance.
Declaration of interests
This study was partially motivated by the fact that I was running low on mechanical pencils. However, this motivation and my preference for mechanical pencils did not influence the results of this study.