Gaussian Distrib: What is Standard Deviation of Mean?

[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. length of an object) or set of data(e.g. lenghts of objects)?

 

[analogdesign]

Check out Wikipedia, it has an excellent discussion of the Gaussian distribution.

If that is too technical to start, here is a nice simplified explanation:

http://math.about.com/od/glossaryofterms/g/Bell-Curve-Normal-Distribution-Defined.htm

 

[A David]

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

 

[statdad]

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. length of an object) or set of data(e.g. lenghts of objects)?

Answered in the first point of this reply.

 

[blue_raver22]

The standard deviation of the mean is a measure of how spread out the data is around the average value, or mean, of a set of measurements. It represents the average distance of each data point from the mean. In a Gaussian distribution, approximately 68% of the measurements will fall within one standard deviation of the mean. This means that most of the data will be clustered around the average value, with some data points falling further away from the mean.

When they say "measurements," they are referring to individual data points. So, if you have a set of measurements, such as lengths of objects, the standard deviation of the mean will tell you how close the lengths are to the average length. This is useful in understanding the variability of the data and can help in making predictions or drawing conclusions from the data.