Key relationship
y=mx+b; |δy|≤LC/2; δm=δy/x when x,b are exact.
Physics · Practical apparatus
Graph scales and error bounds
Select graph scale through the measured range, correct a systematic zero shift and compare resolution bounds with inferred slope. The plotted staircase shows finite instrument divisions.
Open the interactive experiment →Graph scales and error bounds
பூஜ்யப் பிழையைத் திருத்தி அளவீட்டு எல்லையுடன் வரைபடம் வரையவும். சிற்றளவு காரணமாக y-க்கு ±LC/2 எல்லை உண்டு.
Key notes, relationships and model limits
Practical tip
Select graph scale through the measured range, correct a systematic zero shift and compare resolution bounds with inferred slope. The plotted staircase shows finite instrument divisions.
Common trap
A displayed worst-case bound is not a statistical confidence interval. The slope bound assumes exact x and a known intercept.
Model limits
line fitting from a selected point with exact x and known intercept, deterministic nearest rounding. Bounds are not a statistical confidence interval. Displayed bounds are readouts; no random sample is invented.
What you will learn
Adjust graph scales and error bounds apparatus, observe its reading and derive the indicated physical quantity.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
At x=5 s, δy=±0.05 m gives δm=±0.01 m/s if x and intercept are exact.
Why this matters
The model connects graph scales and error bounds with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
A 0.1 m division gives nearest-rounded y bound?
- ±0.1 m.
- ±0.05 m.
- ±0.2 m.
Read the explanation
±0.05 m.
Course connection: Virtual apparatus preparation. Check exact board/exam membership in the syllabus sources. Physical practical work remains necessary.