A normal distribution of data means
that most of the examples in a set of data are close to the
"average," while relatively few examples tend to one
extreme or the other.
If you looked at normally
distributed data on a graph, it would look something like this:
standard deviation is a statistic that tells you
how tightly all the various values are clustered around
the mean in a set of data.
red area on the above graph is one standard deviation
away from the mean in either direction on the horizontal
axis and accounts for about 68% of the values in the set
of data. Two standard deviations away from the
mean is shown by the red and green areas and
accounts for roughly 95 percent of the values. Three
standard deviations (the red, green and yellow areas)
account for about 99 percent of the values.