A student measures the time period of 100 oscillations of a...

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is $90 \mathrm{~s}, 91 \mathrm{~s}, 95 \mathrm{~s}$, and $92 \mathrm{~s}$. If the minimum division in the measuring clock is $1 \mathrm{~s}$, then the reported mean time should be: (A) $92 \pm 5.0 \mathrm{~s}$ (B) $92 \pm 1.8 \mathrm{~s}$ (C) $92 \pm 3 \mathrm{~s}$ (D) $92 \pm 2 \mathrm{~s}$

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is $90 \mathrm{~s}, 91 \mathrm{~s}, 95 \mathrm{~s}$, and $92 \mathrm{~s}$. If the minimum division in the measuring clock is $1 \mathrm{~s}$, then the reported mean time should be:
(A) $92 \pm 5.0 \mathrm{~s}$
(B) $92 \pm 1.8 \mathrm{~s}$
(C) $92 \pm 3 \mathrm{~s}$
(D) $92 \pm 2 \mathrm{~s}$

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Key Concepts

Mean (Average Value)

The mean is a measure of central tendency calculated as the sum of all measurements divided by the number of measurements. In experimental work, the mean provides an estimate of the true value when several observations are made, helping to smooth out random fluctuations in the data.

Measurement Uncertainty

Measurement uncertainty quantifies the doubt about the result of a measurement. It includes both random errors, which can be reduced by taking multiple readings, and systematic errors arising from the limitations of the instrument, such as the resolution indicated by its least count.

Least Count

The least count is the smallest division or the minimum measurable value that an instrument can reliably indicate. It sets a lower bound on the precision of measurements and is used to estimate the basic uncertainty associated with each reading due to the instrument's resolution.

Error Propagation

Error propagation involves determining how uncertainties in individual measurements combine to produce an overall uncertainty in a calculated result. When averaging multiple measurements, the individual uncertainties and the spread of the data (random errors) are combined to report the final uncertainty in the mean value.

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