We time every run and we never trust a single number. Six runs, a mean, a range, and one suspicious result that has to be argued about. Then the split times from the timing gates become a distance–time graph, and the gradient tells you how fast the car was going along the lane.
Calculate mean, median and range for a set of race times and choose which one to report.
02
Identify an outlier, justify excluding it, and recalculate.
03
Plot a distance–time graph from timing-gate splits and read speed from the gradient.
04
Explain why you need repeated runs before you can call a design change an improvement.
02From the Nightmare car
Every test day produces a sheet like the one in Fig. 7. Six runs of the same car, the same batch of cartridges, the same launcher. Five of them agree to within a few hundredths of a second. One does not. That run had a slow launch trigger and we all saw it happen. The question is what to do with it. Our rule is that a result is only left out if there is a physical reason written on the sheet, and the mean of what is left is what we compare against the next design change. The timing gates every 5 m give a second picture: split times, which become a distance–time graph.
Fig. 7 Left: six runs of the same set-up. Run 5 is left out for a written physical reason and the mean of the other five is reported. Right: the timing-gate splits plotted as distance against time. The gradient of each segment is the average speed over that 5 m.
03Core idea
Three summaries, one decision
mean = Σx / n · median = middle value when sorted · range = largest − smallest
The mean uses every value, so one bad run drags it along. The median ignores the extremes, so it is a good check on the mean. The range tells you how repeatable the car is. A small range is worth as much as a fast mean, because a car that is only sometimes fast loses knockout races.
Outliers
A value a long way from the rest is an outlier. We flag anything more than about 10% away from the median. Flagging is not the same as dropping. A run is only dropped when there is a physical reason, such as a slow trigger, the car touching the lane wall, or a cartridge misfire. Otherwise it stays in and the mean is honest.
Gradient is speed
speed over a segment = Δx / Δt This is the gradient of the distance–time graph between two gates.
A straight line means a steady speed. A line that curves upwards means the car is speeding up, and a line that flattens means it is slowing down. Our runs curve hard in the first 5 m, while the cartridge is pushing, and are nearly straight after that. That is exactly what LAB-05 predicts.
i
Why six runs? One run tells you what happened once. Three runs give you a rough mean. Six runs let you see the range and spot a bad launch without guessing. More than ten and you have used a lot of cartridges for a small gain in confidence.
04Timing-gate analyser
Type in your own run times or use ours. The analyser works out the summaries, flags a suspected outlier, and lets you leave it out to see the effect. Below that, edit the split times to rebuild the distance–time graph and read each segment’s gradient.
A. Six runs
Run
Time (s)
Speed (20 m ÷ t)
Flag
—sMean
—sMedian
—sRange
—sBest run
B. Splits from the gates
Gates at 0, 5, 10, 15 and 20 m. Enter the time the car crossed each gate.
Gate (m)
Time (s)
Segment speed (m/s)
Segment speed = Δx / Δt, the gradient between that gate and the one before it.
05Worked example
Six runs: 1.212, 1.184, 1.239, 1.196, 1.620, 1.203 s.
Sorted: 1.184, 1.196, 1.203, 1.212, 1.239, 1.620
Median = (1.203 + 1.212) / 2 = 1.2075 s. The 1.620 s run is 34% above the median, so flag it.
Mean of 6 = 7.654 / 6 = 1.276 s. Mean of 5, with run 5 left out for the slow trigger, = 6.034 / 5 = 1.207 s
Range of 5 = 1.239 − 1.184 = 0.055 s
Report: 1.207 s, the mean of five runs, with one run left out for a slow launch trigger. The run that was left out still stays on the sheet.
Gradient between the 10 m and 15 m gates: t = 0.620 s and 0.850 s.
Compare that with the first segment: 5 / 0.390 = 12.8 m/s. The car’s average speed more than doubles between the first and third segments. The graph curves, then straightens out.
06Student questions Teacher mode is off. Answers are hidden.
Q1 · Summarise[3]
Five runs: 1.221, 1.198, 1.205, 1.231, 1.190 s. Find the mean, median and range.
Answer key
Sorted: 1.190, 1.198, 1.205, 1.221, 1.231
Mean = 6.045 / 5 = 1.209 s · Median = 1.205 s · Range = 0.041 s
Q2 · Judge[3]
A seventh run records 1.05 s, the fastest ever. The launcher operator says nothing unusual happened. Should it be left out? What should the team do next?
Answer key
No. There is no physical reason to leave it out, so it stays in the data (1). But one fast run is not evidence of a faster car. The team should repeat the run, at least three more times, to see whether it happens again (1). If it never happens again, it stays on the sheet as an unexplained result and the median is reported next to the mean (1).
Q3 · Gradient[3]
The car crosses the 15 m gate at 0.850 s and the 20 m gate at 1.078 s. Find the average speed over the last segment. Is the car still accelerating? How do you know?
Only just. It was 21.7 m/s on the previous segment and is 21.9 m/s now (1). The graph is almost straight, so the car has stopped gaining speed. The thrust ended long ago and drag is balancing what is left (1).
Q4 · Explain[2]
Why does Team Nightmare report the mean of several runs rather than the best run when comparing two body designs?
Answer key
The best run is partly luck, from the launch and the cartridge. The mean averages that out, so the comparison is about the car and not about the day (1). A design is only called faster if its mean beats the other mean by more than the range of either set (1).
07Printable worksheet The answer key prints as well when teacher mode is on
Team Nightmare · STEM Subject Lab
NM-LAB-07 · Race Data & Graphs
Name ______________________ Class __________ Date __________
Maths · Data 40 minutes Links to LAB-05
Formula bank
mean = Σx / n
median = middle of sorted list
range = max − min speed = Δx / Δt
House rule
Flag a run that is far from the others. Only leave it out if there is a physical reason written on the sheet.
meanmedianrangeoutliergradientrepeatable
[3]1.Six runs of configuration B: 1.212, 1.184, 1.239, 1.196, 1.620, 1.203 s. Sort them, then find the median and the range of all six.
[2]2.Which run would you flag as an outlier, and by roughly what percentage does it differ from the median?
[3]3.The run sheet says “run 5: slow trigger”. Calculate the mean of the remaining five runs. Write the sentence you would put in the report.
[4]4. Plot.Gate times for one run: 0 m → 0.000 s, 5 m → 0.390 s, 10 m → 0.620 s, 15 m → 0.850 s, 20 m → 1.078 s. Plot distance (vertical) against time (horizontal) on the grid and join the points.
[3]5.From your graph (or the gate times), calculate the average speed between 5 m and 10 m, and between 15 m and 20 m. What does the change tell you?
Accept any equivalent working. The marks in brackets match the student sheet.
Teacher copy Do not hand out
1. [3] Sorted: 1.184, 1.196, 1.203, 1.212, 1.239, 1.620 (1). Median = (1.203 + 1.212)/2 = 1.2075 s (1). Range = 1.620 − 1.184 = 0.436 s (1).
2. [2] Run 5, 1.620 s (1); (1.620 − 1.2075)/1.2075 ≈ 34% above the median (accept 30–35%) (1).
3. [3] Mean of 5 = (1.212 + 1.184 + 1.239 + 1.196 + 1.203)/5 = 6.034/5 = 1.207 s The sentence must give the value, say it is a mean of five, and say why one run was left out. For example: “Configuration B averaged 1.207 s over five runs. Run 5 (1.620 s) was left out because of a slow launch trigger.” One mark each for the value, the method and the reason.
4. [4] Five points in the right places (2). Joined in order (1). The line rises steeply and then straightens. Accept straight segments (1).
5. [3] 5–10 m: 5 / (0.620 − 0.390) = 5 / 0.230 = 21.7 m/s15–20 m: 5 / (1.078 − 0.850) = 5 / 0.228 = 21.9 m/s The speed is almost constant over the second half. The car finished speeding up early, and the graph is nearly a straight line (1).