# Understanding Standard deviation in Normal Distribution

My question is going to be very basic/ beginner level . I have trouble understanding the following :

A normal distribution is said to be defined by its mean and Std.deviation . My question is Shouldn't that " Standard deviation " apply to the whole of the data ? i.e , that standard deviation is how much the data differs from its mean on average .

But , why do we say "68% of the data lies within 1 standard deviation , 95% data lie within 2 standard deviations .. and so on " ?

Shouldn't 100% of the data lie within the original standard deviation of the data ? We calculate the standard deviation only from the given data , then why do we say " Only 68% of it lies within 1 standard deviation and so on " ?

Mine is a very basic question but I have trouble understanding this .Can someone please provide an intuitive explanation as to what's happening here ?

• why do you think SD should include all the data inside its range? – hbadger19042 Jul 11 '20 at 12:20
• Because the standard deviation itself was calculated from the given data ? I am not sure – Bharathi Jul 11 '20 at 12:27
• The mean is also calculated from all of the given data but it doesn't include anything. – hbadger19042 Jul 11 '20 at 12:37