I was thinking about Chebyshev's Inequality when k=1, which gives an upper bound of up to 100% of the data lying outside one standard deviation.
I was trying to think of an example of a distribution where this was actually true though, and I can't.
Can someone give an example of a simple dataset or distribution in which none of the data lies within one standard deviation?
Or can I prove it's not possible? (Apologies if this is obvious, I am trying to self-teach statistics)
I feel like I am missing something obvious...