Question

If I have a data set that overall is symmetric and I add a data point that is very high, what will happen to the mean?
A) The mean will decrease.
B) The mean will increase.
C) The mean will be raised by one data point value.
D) The mean will not change unless that data point was already in the data set.

Answer 1

Simple example: mean of {1,1} is 1. mean of {1,1,3} is greater or smaller than 1?

Answer 2

The mean is a NON-ROBUST estimator, this means that the outliers will have a bigger impact on that statistic than if you use say the median. The mean is just \( \mu=\sum_{i \in n} \frac{X_i}{n} \). If you add something big there, say a number bigger than the existing mean, you will get \( \mu_1 = \frac{n\mu_0 +s}{n+1} >= \mu_0 \), hence it will increase if the data point is larger than the previous mean.