Graphing: plotting, best-fit lines & gradients
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All 11 Flashcards — Graphing: plotting, best-fit lines & gradients
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Question
What is a line of best fit?
Answer
The single **straight line** drawn as close as possible to all the plotted points, with roughly as many points above it as below. You read the physics off this line.
Question
What does an error bar on a point show?
Answer
The **uncertainty** in that measurement — the true value could lie anywhere along the bar.
Question
How do you read a gradient off a graph?
Answer
Pick **two far-apart points ON the line** and compute **rise ÷ run**: $m = \Delta y / \Delta x$. Use the line, not the data points.
Question
How do you find the uncertainty in a gradient?
Answer
Draw the **steepest** and **shallowest** straight lines that still pass through all the error bars, then $\Delta m = (m_{\max} - m_{\min}) / 2$.
Question
Uncertainty rule for multiplying or dividing (y = ab/c)?
Answer
The **fractional** uncertainties add: $\Delta y/y = \Delta a/a + \Delta b/b + \Delta c/c$. **Given** in the data booklet.
Question
Uncertainty rule for a power (y = aⁿ)?
Answer
Multiply the fractional uncertainty by the size of the power: $\Delta y/y = |n|\,\Delta a/a$. **Given** in the data booklet.
Question
Uncertainty rule for adding or subtracting (y = a ± b)?
Answer
The **absolute** uncertainties add: $\Delta y = \Delta a + \Delta b$. Built from the booklet rules.
Question
What physics does the gradient of a graph usually give?
Answer
A relationship between the two plotted quantities — e.g. a **spring constant**, a **speed** (distance–time), or a **refractive index** (depending on what is plotted).
Question
What does the intercept of a best-fit line tell you?
Answer
The value of y when x = 0 — often a physical quantity, or, if it should be zero, a sign of a **systematic offset** (zero error).
Question
Why use a graph instead of just one calculation?
Answer
The best-fit line **averages out random scatter** across many readings, giving a more reliable value and letting you spot anomalies and offsets.
Question
To how many significant figures do you quote an uncertainty?
Answer
Usually **one** significant figure, and round the value to the same decimal place as the uncertainty.
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Full study notes for Graphing: plotting, best-fit lines & gradients
Topic 6.1 hub
Experimental skills
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