Expert: Josh - 4/2/2008

Question
I am trying to help my daughter with her homework, but I cannot understand the concept of outliers. They give a set of number. 50,150,150,200,200,200,200, 300,300,300, 350,350, 400,400,400,450,500. and asks
What is the outlier?  and
Does the outlier raise or lower the mean?

Answer
Hi Maricela,

An outlier is basically a data point which does not conform to the observed trend. If we include such extreme data point(s) when we calculate a statistic, such as the mean or standard deviation, it will skew our result.

Without any formal analysis, I think the sample with value "50" would be an example of an outlier. You can calculate the mean using the remaining samples, excluding the data point "50", and repeat the exercise again, including the outlier. See what difference it makes. You should find that the outlier, in this example, has an effect of lowering the average.

In the first instance, i.e., excluding the sample point "50", the mean is 303.1250. In the second instance, including the sample point "50", the mean works out to be 288.2353.

Assuming the data follows a normal distribution (bell shape histogram), we can define an outlier as a sample lying beyond some number of standard deviation about the mean. In this question, the mean and standard deviation are 303.125 and 110.25 respectively.

The data point x[n]=50 is (50-303.125)/110.25 = -2.29 (more than two) standard deviation below the mean value.