Why does Uniform Distributions have no outliers? I was reading about the relation between Kurtosis and Outliers on Wiki and got across a line 'An example of a platykurtic distribution is the uniform distribution, which does not produce outliers' [here]https://en.wikipedia.org/wiki/Kurtosis
I mean it would also have some µ ± 2σ cut in probability density curve, then how can U.D not have outliers?  
 A: Let's take a look at the uniform distribution.  Here is some R code, stuff after a # is a comment:

set.seed(1234)
random <- runif(1000, min = 0, max = 10)
sd(random) mean(random) + 2*sd(random)  #10.89 mean(random) -
  2*sd(random)  #-0.75

So, we see that there is no value in this data set that is more than 2 SD above the mean or less than 2 SD below.
This is true even for much larger N.
For a Normal distribution with large N, some values will be outside the 2 SD range, but these are not outliers. An outlier is an unexpected value. If we have a Normal distribution with a large N, then we expect some values to be beyond 2 SD. Indeed, for a perfectly Normal distribution, about 5% of the values will be outside this range.  Thus

set.seed(1234)
random <- rnorm(100000, 0, 1)
sd(random) sum(random > mean(random) + 2*sd(random))  #2389 sum(random
  < mean(random) - 2*sd(random))  #2235

and we even expect (and get) some beyond 3 SD:

sum(random > mean(random) + 3*sd(random))  #143 sum(random <
  mean(random) - 3*sd(random))  #127

The 2 SD rule worked okay as a rule of thumb in the old days, when "big data" meant a few thousand cases. 
