Direct proportionality with random errors

Steps:

• Direct proportionality means q = k p, so the graph is a straight line through the origin.
• Random errors in measurements cause data points to deviate unpredictably from this line.
• Identify the graph where points cluster around a straight line but scatter randomly.
• Eliminate graphs with perfect alignment, offsets, or curves.

Why C is correct:

• Random errors produce scatter around the ideal straight line, as defined by the error distribution in experimental data following q = k p.

Why the others are wrong:

• A shows a perfect straight line, indicating no errors.
• B shows a line not through the origin, suggesting systematic error like zero offset.
• D shows a curve, indicating non-proportional relationship or systematic nonlinearity.

Final answer: C