Linearising and Analysing Data — practice questions

A student suspects $y = kx^2$. State what should be plotted on each axis to produce a straight line, and what the gradient of that line represents.

A log–log plot of resistance $R$ against wire length $l$ gives a straight line with gradient $1.0$. Explain what this shows about the relationship between $R$ and $l$.

A student plots raw bounce height $h$ against drop height $H$ and gets a curve that looks almost straight near the origin. They conclude the relationship is linear without linearising. Evaluate this conclusion.

Three repeated length measurements are $20.1$ cm, $20.3$ cm, $19.9$ cm. Find the mean and the uncertainty using half the range.

Explain the difference between the reliability and the validity of an investigation, using an example of an investigation that could be reliable but not valid.

A student's best-fit line through error-bar data has gradient $2.1$. The steepest acceptable line (through the error bars) has gradient $2.4$, and the shallowest has gradient $1.8$. State the gradient with its uncertainty, and explain what this uncertainty means for the student's conclusion about the power $n$ in $y = kx^n$.