Normal distribution and 68-95-99

[Jarwulf]

hi, i need to know on intuitive terms why roughly 68% of a randomly sampled population falls within 1 standard deviation of the mean and 95% within 2 sd etc. There doesn't seem to be any explanations on the web besides blurting out CLT or some hocus pocus with arcane calculus symbols. Thanks

[CaptainPanic]

Isn't the standard deviation just a definition?

 

It's like asking why a meter is exactly 100 centimeters? It's because we defined it to be like that.

[imatfaal]

The wikipage on the 68-95-99.7 rule says the following

 

In statistics, the 68-95-99.7 rule — or three-sigma rule, or empirical rule — states that for a normal distribution, nearly all values lie within 3 standard deviations of the mean.

 

Note the third name - the empirical rule. The Standard deviation is a defined calculation, and the normal distribution just is; there is no ulterior motive or design - just a very useful consequence

[ewmon]

There's the Central limit theorem and Central tendency.