Question

The observations of 124.53, 124.55, 142.51, and 124.52 are obtained when taping the length of a line. What should the observer consider doing before a mean length is determined from the set of observations?

Answer 1

Answer: the observer should consider to eliminate or to retake the third measure.

Explanation:

The four measures taken are 124.53, 124.55, 142.51 and 124.52.

As it can be easily seen, the third measure is much different from the other three. This means that something went wrong during the observation: it can be either the measure taken wrong or that the number was written wrong (if you switch the 2 and the 4 you get a number similar to the other ones).

If the third measure is not considered, an estimate of the mean would place it around 124.5, while if the outlier (the detatched number) is considered an estimate of the mean would increase to about 129.

Therefore, in order to obtain a more reliable mean, the observer should consider to eliminate or to retake the third measure.