Question

Outliers have VERY LITTLE OR NO EFFECT on which of the following

Answer 1

Answer: median and mode

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Explanation:

Imagine we had the set {1,2,3,4} where all the values are clumped or clustered together fairly closely. Computing the range, median, mode, mean and population standard deviation yields the following

• range = 3
• median = 2.5
• mode = none
• mean = 2.5
• population standard deviation = 1.118 approximately

Now lets add in a very large outlier, say 1000, and we now have this set: {1,2,3,4,1000}

For this new set, recompute the range, median, mode, mean and population standard deviation

• range = 999
• median = 3
• mode = none
• mean = 202
• population standard deviation = 399.001 approximately

We can see that the range, mean and standard deviation have increased significantly. The median has gone up but not by much. The median is not greatly affected by outliers which is why the median is used for home prices for instance. The mode is also not affected because imagine if we had the set {1,1,1,2,3,4} and we can see the mode is 1 as it occurs the most times. Add in a very large outlier (again say 1000) and we now have {1,1,1,2,3,4,1000}. The mode is still 1 because it still occurs the most frequent of all the values. We see that the mode is far more robust as it hasn't changed at all while the median did change.