Undergrad Connection between mean and median

[dextercioby]

TL;DR

See title and problem below.

I have 100 random real (even rational with only one decimal, like average temperatures of months at a particular weather station) numbers. With them I compute the arithmetical mean and the median. It is a (very) small probability they are the same number within let's say 0,1 or 0,2.

Question. If I let the number of items increase (let us say 1000 instead of 100), is it more probable that the difference between the mean and the median decreases? It is true that for a very, very large number of numbers this difference is arbitrarily close to 0, FAPP is 0?

 

[mathman]

Mean and median will only be the same for a distribution symmetric around the mean. Example: (0,1,10) has a median of 1 and a mean of 11/3.

 

[malawi_glenn]

I think that only applies to symmetric distributions, that the mean and median will approach the same value for very very large data sample.

Mean and median will only be the same for a distribution symmetric around the mean. Example: (0,1,10) has a median of 1 and a mean of 11/3.

The question was what will happen if you have very very large dataset. Your example has three numbers.

 

[Office_Shredder]

I think that only applies to symmetric distributions, that the mean and median will approach the same value for very very large data sample.The question was what will happen if you have very very large dataset. Your example has three numbers.

No, they're suggesting a distribution that takes three values with equal probability