Random Error And Mean

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A student records the period of an oscillating spring four times as 2.01 s, 2.05 s, 1.99 s and 2.03 s during a laboratory session. What is the best estimate of the true period from these readings?

RankGuru · Accepted Answer

NCERT Class 11, Chapter 2 (Units and Measurements) explains that random errors fluctuate in sign and magnitude between trials, and the best estimate of the true value is obtained by taking the arithmetic mean of repeated readings. Averaging the four periods gives (2.01 + 2.05 + 1.99 + 2.03) / 4 = 8.08 / 4 = 2.02 s. The option 2.05 s is wrong because it selects only the largest single reading rather than averaging. The option 1.99 s is wrong as it picks only the smallest reading, ignoring the others. The option 2.10 s is wrong since it exceeds every individual measurement and cannot be an average of them. A final plausibility check confirms that the mean value 2.02 s lies comfortably within the spread of the readings, which is exactly what we expect when averaging measurements affected only by random error.

Random Error And Mean

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