Gaussian distribution!

lover-of-light
In my course textbook it is written that "approximately 68% of the measurements from a normally distributed set lie within +-1 standard deviation of the mean value".
What do they mean by standard deviation of the mean value? They give a definition for "the mean"(of a set of measurements(data)) right before talking about gaussian distribution.
Also when they say "68% of the measurements" do they use the word "measurement" as in the meaning of data(e.g. lenght of an object) or set of data(e.g. lenghts of objects)?

A David
You can think of the standard deviation as "the average distance from the average."

Homework Helper
In my course textbook it is written that "approximately 68% of the measurements from a normally distributed set lie within +-1 standard deviation of the mean value".
What do they mean by standard deviation of the mean value? They give a definition for "the mean"(of a set of measurements(data)) right before talking about gaussian distribution.
Here they are talking in terms of distance: roughly 68% of the measurements are within a distance of one standard deviation of the mean. If you think of a sketch of a bell curve, then when you locate
the two values $\mu - \sigma$ and $\mu + \sigma$, you can say that roughly 68% of the values from that distribution is between those two values

Also when they say "68% of the measurements" do they use the word "measurement" as in the meaning of data(e.g. lenght of an object) or set of data(e.g. lenghts of objects)?