Comment, using two points on your line of best-fit, whether or not this is a valid hypothesis.

Suggest why using two points cannot confirm that \({h_{{\text{mean}}}}\) is proportional to \({T^2}\).

The temperature is measured using a liquid in glass thermometer. Explain why it is likely that the uncertainty in \(T\) is constant.

coordinates of two points on the line correctly read from the graph; } (check points read to within half a square and ignore omission of powers of ten in reading)

\(\frac{{{T^2}}}{h}\) or \(\frac{h}{{{T^2}}}\) calculated for both values;

consistent conclusion that values similar within the (typical) experimental error so sensible / differ outside (typical) experimental error so not sensible;} (must see reference to experimental error not just bald statement)

Award [2 max] for a graph of \({h_{{\text{mean}}}}\) versus \({T^2}\) and a conclusion that hypothesis is not valid.

Do not award credit for “does not go through origin”.

two points define a straight line / any arbitrary curve can pass through two points; to confirm hypothesis third point (or more) must lie on the straight line;

or

refers to experimental error in data (and therefore error in ratio) / depending on the two points chosen the hypothesis may be confirmed;

increasing the number of data points increases the strength of conclusion;

or

one of the two points chosen may be anomalous/erroneous/outlier;

third point needed to confirm hypothesis;

same thermometer used;

same eyes used;

same reading method used;

this type of thermometer has (typically) equal graduations;

liquid in thermometer expands linearly;

Many read two points correctly from the line, but too often examiners saw lines that missed a data point with the printed point still being used for the read-off. These derived data then generally led to a correct evaluation of \(\frac{h}{{{T^2}}}\) (or it’s reciprocal). However, for full marks, the examiners needed to see some consideration of the (sometimes considerable) error represented by the error bars and this was only rarely present.

There were a number of alternative statements that could gain credit here. The most frequently seen suggestion was that, because two points can define a line of any curvature, therefore a third (or more) data point is required to establish the proportionality.