Scientific Reasoning and Experimental Data Analysis
Scientific reasoning and data analysis questions test whether you can design a fair test and read evidence without overclaiming. Expect variables, controls, accuracy versus precision, uncertainty, significant figures, graphing, slope interpretation, and correlation versus causation.
Core rules
- Independent variable: what you change; dependent variable: what you measure; controlled variables: held constant.
- Accuracy is closeness to the true value; precision is repeatability. A precise set of measurements can still be inaccurate if there is systematic error.
- Report uncertainty to one significant figure and match the decimal place of the mean. Do not gain precision by averaging.
- On a linear graph, slope = rise/run and carries units from the axes. A best-fit line reduces the influence of random scatter.
- Correlation does not establish causation; a controlled experiment or a plausible mechanism is needed.
Worked example
A spring is loaded and its extension measured. At 2.0 N the extension is 0.10 m; at 6.0 N it is 0.30 m. Find the spring constant. Plot force on the y-axis and extension on the x-axis. Slope = (6.0 − 2.0) N / (0.30 − 0.10) m = 4.0/0.20 = 20 N/m. Hooke’s law F = kx gives k = 20 N/m. Using a single point would ignore scatter; the two-point slope uses the linear trend.
Traps
- Swapping independent and dependent variables on a graph.
- Calling repeated measurements accurate when they are merely precise.
- Dropping units from a slope or failing to convert cm to m.
- Keeping too many significant figures in a final answer.
- Concluding causation from an observational correlation.
- Choosing an outlier as representative instead of checking it.