Question

4. Consider a data set of 1000 annual incomes (in thousand of dollars). Suppose two zeros were mistakenly added to one of the incomes, making it 100 times the correct amount. How would this affect the mean and median? Underline the correct choice:

Question: b. The [mean, median] would be changed very little or not at all, depending on whether the changed observation was below or above the [mean, median]. That is, the [mean, median] is robust.

Answer 1

We know that mean is the average of all data values, so it will be affected most and we know that median is just the middle value of the data set, so it is affected least.

In given case, where we have one outlier, mean will be affected most and median will not be affected at all

So, answer is given as

The median would be changed very little or not at all, depending on whether the changed observation was below or above the median. That is, the median is robust.