# Gaussian distribution!

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)?

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

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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)?