Tools and Inquiry — IB Physics skills
T.3.9 Determining Uncertainties from Graphs — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 14 of 22 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
T.3.9 Determining Uncertainties from Graphs — IB PHYSICS SL notes: Use error bars and best and worst fit lines to find uncertainties in gradients and intercepts.An uncertainty (error) bar shows the absolute uncertainty of a plotted value — drawn above and below a point or side to…
- More precise measurements have shorter bars
- Bars need not all be the same size
- Plot bars in both directions when both variables have uncertainties
- Consistent with the data
- Common data-based question
- Draw both worst lines if needed
Part 1 of 7Uncertainty bars
1An uncertainty (error) bar shows the absolute uncertainty of a plotted value
- An uncertainty (error) bar shows the absolute uncertainty of a plotted value drawn above and below a point or side to side.
2More precise measurements have shorter bars
- More precise measurements have shorter bars less precise ones have longer bars.
3Bars need not all be the same size
- Bars need not all be the same size each point can have a different uncertainty.
4Plot bars in both directions when both variables have uncertainties
- Plot bars in both directions when both variables have uncertainties or in one if one is negligible.
Part 2 of 7Testing a relationship with error bars
1
A relationship is linear if a straight line can pass through all the error bars.
2
It is non-linear if a smooth curve can pass through all the bars but a straight line cannot.
3Consistent with the data
- Consistent with the data the line of best fit should pass through all the error bars.
4Common data-based question
- Common data-based question is a proposed relationship consistent with the data?
Part 3 of 7Best and worst fit lines
Best and worst fit lines
The best line of best fit passes as close as possible to all the points.
The worst fit line is the steepest or shallowest line that still passes through all the error bars.
- The worst gradient is the one differing most from the best gradient.
Draw both worst lines if needed
- Draw both worst lines if needed then find their gradients.
Part 4 of 7Uncertainty in the gradient
1Percentage uncertainty in gradient
|best gradient − worst gradient| / best gradient × 100%.
2Absolute uncertainty in gradient
(max. gradient − min. gradient) / 2.
3Use large gradient triangles on all lines
- Use large gradient triangles on all lines to reduce reading errors.
4Quote the gradient with its uncertainty and units
- Quote the gradient with its uncertainty and units to one significant figure for the uncertainty.
Part 5 of 7Uncertainty in the intercept
Uncertainty in the intercept
Percentage uncertainty in y-intercept
|best intercept − worst intercept| / best intercept × 100%.
Absolute uncertainty in y-intercept
(max. intercept − min. intercept) / 2.
An intercept consistent with zero within uncertainty suggests direct proportionality.
Part 6 of 7Procedure for a graph with error bars
1
Draw sensible scales on the axes and plot the data.
2
Draw the error bars for each point.
3
Draw the line of best fit.
4
Draw the line of worst fit within all the bars.
5
Find the gradient of each line using large triangles.
6
Calculate the percentage uncertainty in the gradient.
- Typical numbers
- best gradient 0.25 and worst 0.28 give 12%.
Part 7 of 7More from the specification
More from the specification
Graphical determination of speed and power
- Graphical determination of speed and power evaluating maximum and minimum gradient slopes determines experimental uncertainty in vehicle speed and rate of power.
Types of experimental uncertainties
- Experimental measurements entail systematic errors and random errors (unpredictable experimental fluctuations).
- (instrument calibration offsets)
Error bars and graphical worst-fit lines
- Graphical uncertainty analysis involves plotting data error bars and fitting maximum/minimum gradient lines to determine parameter bounds.
Propagation of uncertainties in calculations
- Absolute uncertainties add when quantities are summed or subtracted,
- whereas percentage uncertainties add when quantities are multiplied or divided.
Vector magnitude and direction
- Vector magnitude and direction vector physical quantities like displacement and force require both numerical magnitude and spatial direction.
Resultant vector addition
- Resultant vector addition adding perpendicular component vectors via Pythagoras equation determines overall magnitude of resultant force or distance.
Error bars in vector graphs
- Error bars in vector graphs error bar length denotes experimental uncertainty in measured vector quantities on Cartesian coordinate plots.
Derived unit
- A unit formed by multiplying or dividing SI base units.
Scale drawing
- Accurate drawing with a chosen scale.
Parallelogram method
- Vector addition using a parallelogram of vectors.
Vector
- Quantity with magnitude and direction.
Resultant
- Vector sum of two or more vectors.
Distance
- Total length of path travelled, a scalar.
Length
- Resistance is directly proportional to the length of a wire.
Constant
- Not changing.
Displacement
- Change in position.
Scalar
- Quantity with magnitude only.
Resultant vector
- Single vector equivalent to a combination of vectors.
a
− ω2x
What the symbols mean: a = acceleration (m s−2) · ω = angular frequency (rad s−1) · x = displacement from equilibrium (m); the minus sign means a always points back to the centre
Key terms
| Term | Meaning |
|---|---|
| Error bar | Line on a graph showing the absolute uncertainty of a point. |
| Best fit line | Line passing as close as possible to all points. |
| Worst fit line | Steepest or shallowest line passing through all the error bars. |
| Gradient uncertainty | Spread in gradient from best and worst fit lines. |
| Intercept | Value of y where the line crosses the y-axis. |
| Consistent | Line can pass through all the error bars. |
Avoid these mistakes
1
Drawing all error bars the same size — each point has its own uncertainty.
2
Using the largest gradient instead of the one that differs most from the best.
3
Forgetting that the worst line must still pass through all the error bars.
4
Dividing by the worst gradient instead of the best gradient.
5
Using a small triangle for gradient — this increases the reading uncertainty.
Marked practiceQuizzes for this lesson
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