Uncertainty in gradients
The uncertainty in the gradient (or slope) of a graph, determined by drawing maximum and minimum gradient lines (lines of best fit with the steepest and least steep slopes that pass through all error bars). The uncertainty is half the difference between maximum and minimum gradients.
Formula
Uncertainty = (max gradient − min gradient) / 2
Real World
Engineers at Rolls-Royce testing jet engine blade fatigue plot stress vs. cycles graphs with error bars, using gradient uncertainty to determine whether a blade's lifetime falls within safe operating limits.
Exam Focus
Always draw both max and min gradient lines through all error bars — examiners penalise using only the best-fit line.
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