Question

In each of the following data sets, tell whether the outlier seems certain to be due to an error or whether it could conceivably be correct.

a. A rock is weighed five times. The readings in grams are 48.5, 47.2, 4.91, 49.5, 46.3.
b. A sociologist samples five families in a certain town and records their annual income. The incomes are $34,000, $57,000, $13,000, $1,200,000, $62,000.

Answer 1

a) There is outlier (lower category), but this outlier seem certain to be due to an error.

b) There is outlier (upper category), this outlier seem certain to be conceivably correct.

Explanation:

a) The outlier in the rock weight is certain to be due to an error. As shown, the rock was weighed five time to ascertain the actual weight or perhaps to known the mean weight. Thus, having a value 4.91 can not be true. It can only be due to an error of recording the values. It suppose to be recorded as 49.1.

b) Since this was a sample of annual income of five different families, it quite possible that a particular family annual income is $1, 200, 000. Hence, we cannot regard this outlier an error, rather conceivably true.

See attached for the box plot of the two data sets.