Significant Figures And Errors

Question

The period of a pendulum is measured five times giving readings that scatter about a mean value, and a student wants to know which error this random scatter represents.

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NCERT Class 11, Chapter 2 classifies measurement errors into systematic, random, and gross types, distinguished by their cause and behaviour. Random errors arise from unpredictable fluctuations such as slight variations in reaction time when starting and stopping a stopwatch, so repeated readings scatter irregularly above and below the true value. Because the fluctuations are equally likely in either direction, taking the arithmetic mean of many readings cancels much of the scatter, which is exactly why several trials are recorded. The option naming systematic error is wrong because systematic errors bias every reading in the same direction and would not produce symmetric scatter. The option naming gross error is wrong because gross errors come from isolated blunders, not a consistent pattern of small fluctuations across all readings. The option naming least count error is wrong because that is the fixed resolution limit of the instrument, not a source of run-to-run scatter. A consistency check confirms that only random errors are reduced by averaging, matching the described repeated-reading strategy.

Significant Figures And Errors

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