An outlier is a data point that is distant from the other observations. For instance, in a data set of {1,2,2,3,26}, 26 is an outlier. There is a formula to determine the range of what isn't an outlier, but just because a number doesn't fall in that range doesnt necessarily make it an outlier, as there may be other factors to consider.
The median is the middle number of a set of numerically ordered numbers. If the number of values in the set is odd, then the median is the central number, with equal amounts of data on both its left and its right. If the set has an even number of values, then the median is the average of the two central numbers. For example, in the set of {1,2,3,4,5,6,7,8}, there is an even amount of numbers, therefore we must find the mean of the two central numbers, which results in
5+42=4.5, the median .
The range r is the distance from the highest value to the lowest value, and is calculated as r=h−l, where h is the highest value, and l is the lowest value. So if we have a set of {52,54,56,58,60}, we get r=60−52=8, so the range is 8.
Given what we now know, it is correct to say that an outlier will affect the range the most. This is because the median is always in the centre of the data and the range is always at the ends of the data, and since the outlier is always an extreme, it will always be closer to the range then the median.
For example, take the set {1,2,3,4,100}, with 100 as the outlier. The range of this set is r=100−1=99, while the median is 3. If we take the outlier 100 out, so the set is now {1,2,3,4}, the range becomes 4−1=3, while the median becomes 3+22=2.5. Evidently, it was the range which was affected the most.
https://mathspace.co/learn/world-of-maths/univariate-data/effects-of-outliers-12017/things-out-of-the-norm-601/
I hope I helped!
