Question

In this class you will need to decide if a data value is unusual (an outlier). You have a way of determining if a datum is an outlier by constructing fences (lower fence = Q1-1.5*IQR, upper fence = Q3+1.5*IQR) and comparing the data value to the value of the fences. If the data value is "outside" one of the fences then it is considered an outlier. For the normal model, some would consider any data value that is more than two standard deviations away from the mean to be an outlier and others would require a data value be more than three standard deviations away from the mean to be an outlier. The "fences" for a normal model are 2.698 standard deviations away (above/below) from the mean. How many standard deviations away from the mean do you think a data value needs to be in ordered to be considered an outlier (unusual) and discuss your reasoning for your choice.

Answer 1

Usually when a data is Normally distributed, the cut off values are -2 and 2.So any point lying outside the interval (-2, 2) have less than 5 percent chance. Hence they are termed as an Outlier. For other Distribution if the sample size is large enough we can approximate it to Normal and thus set the same Cut off values.

For other distribution with small sample size, what we can do is we can calculate Z score by (X-u) /sigma that is by scaling the point and if Z score comes out to be grrater than 2 then it is an outlier. Again this is subjective rule. Some may use 2.5 as cutoff some may use 3 as a cut off. But generally (-2, 2) is good enough