Distinguishing Random and Systematic Errors

Steps:

• Recall that random errors cause unpredictable variations around the true value, while systematic errors consistently bias results in one direction.
• Evaluate option A: Accurate measurements minimize both error types, not requiring small random error.
• Evaluate option B: Precise measurements agree closely but can lack systematic error if unbiased.
• Evaluate option C: Averaging multiple measurements reduces random error by canceling out fluctuations.
• Evaluate option D: Systematic errors shift all measurements consistently, not randomly.

Why C is correct:

• Random errors follow statistical principles where the average of repeated measurements approximates the true value, reducing variability as per the law of large numbers.

Why the others are wrong:

• A: Accuracy means closeness to true value; random error can be large or small independently.
• B: Precision means repeatability; systematic error is possible but not required.
• D: Systematic errors produce consistent bias, not random spread.

Final answer: C