Nature of the observed data and mild and extreme outliers
This question is open to interpretation – I think it’s supposed to be a tricky question so I’m not entirely sure where it’s going. We aren’t actually given any data.
Assuming data normally distributed:
Q 1 Theoretically, does the nature of the observed data have an effect on the definition of what is called “mild” and extreme” outliers?
I don’t have any idea what is meant by “nature” is question 1. Discrete/continuous, perhaps? If so, how?
Q 2 What percentage of values will be “mild” or “extreme” outliers for the observed data?
It seems to me that you can use the definition of 1.5 IQR and 3 IQR to define where the limit between them is by using a Z table. If the mean of a sample is 100 with a SD of 10, then the IQR = 0.675*2 Standard deviations, or 13.5. Therefore, the limit of mild outliers is 6.75 + 13.5*1.5 = 27. So values less than 73 or greater than 127 would be extreme.
BUT – While you can use the assumption of normal distribution to find the probability of an actual outlier, I don’t see that you can make the kind of prediction suggested by Question 2 above.