statistics help

Question

This question is an extension of the ICE distributed in class.

One of the colleges in Florida is called Aviator College of Aeronautical Science and Technology. Its annual tuition and fees were reported in 2015-16 as $73,132, making this college an outlier because it was substantially more expensive than any other college in Florida for that year. 

An outlier is present in the dataset. The paper homework also displays a boxplot and histogram of the dataset. Based on the information available to you, is the median or mean more appropriate as a measure of "average" tuition and fees for Florida?

median or Mean ?

Answer 1

When outliers exist in the dataset, the median is the appropriate statistic to estimate the 'middle' or average of the distribution. This is because when an outlier is present, is can have a dramatic effect on the mean, yet has little to no effect on the median. Consider the following simple example:

Suppose we have the following dataset A: {1 2 3 4 5},

then an error is discovered that changes the dataset to B: {1,2,3 4,25}

the median of both datasets is 3 (the middle observation, however the mean shifts by 4):

mean of A=1+2+3+4+5/5=15/5=3

but the mean of B=1+2+3+4+25/5=35/5=7

It's interesting to note:for dataset A (no outlier), the mean and the median are the same, but in dataset B (has an outlier)the median is 3 (unchanged), but the outlier influences the estimate of the mean from a value of 3 to a value of 7!!