Final answer:
It is possible to obtain measurements with high random error through averaging since random errors cancel out over multiple measurements, improving precision. Larger sample sizes help mitigate the effects of random errors, leading to more precise measurements.
Step-by-step explanation:
Yes, it is indeed possible to obtain measurements when high random errors are present by performing averaging. Random errors cause statistical variability and can differ from one observation to another. If one takes multiple measurements and averages them, the effects of random errors can be minimized, since these errors tend to cancel each other out over a series of measurements. This process improves the precision of the measurements, as precision is dependent upon how closely individual measurements agree with one another.
To ensure accuracy, or how close the average value is to the actual value, one must consider systematic errors separately from random errors. However, in the presence of high random errors, increasing the sample size and taking repeated measurements can mitigate the effects of random errors, leading to more precise, if not necessarily more accurate, measurement results.
Moreover, the concept of uncertainty in measurements reminds us to consider all possible factors that could contribute to measurement uncertainty, such as the quality of the measuring instrument, the conditions under which measurements are taken, and the inherent variability of the subject under study.