Given below are two statements:

Statement I: The standard deviation of a series of repeated measurements estimates the likely size of the chance error in a single measurement.

Statement II: Bias affects all the measurements the same way, pushing them in the same direction.

In the light of the above statements, choose the most appropriate answer from the options given below:

The correct option is Both Statement I and Statement II are true.

Let us analyze the correctness of each statement step-by-step:

Analysis of Statement I:
In statistics and measurement theory, when we make repeated measurements of the same quantity under identical conditions, the values fluctuate due to random variations or chance errors. The standard deviation measures the spread or dispersion of these individual measurements around their average value.
Therefore, the standard deviation directly estimates the typical or likely magnitude of the chance (random) error associated with any single measurement. This makes Statement I true.

Analysis of Statement II:
Bias, also known as systematic error, is a consistent or constant deviation of the measured values from the true value. Unlike random errors, which fluctuate unpredictably in both directions, bias affects all measurements systematically.
It pushes every single measurement in the same direction—either consistently overestimating or consistently underestimating the true value by a similar amount. This makes Statement II true.

Since both statements are correct, the most appropriate choice is that both Statement I and Statement II are true.