What is standard Deviation, what does it show?

The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean (middle or average) in a set of data. When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you you have a relatively large standard deviation.

One standard deviation away from the mean in either direction accounts for somewhere around 68 percent of data. Two standard deviations away from the mean accounts for roughly 95 percent of data. And three standard deviations accounts for about 99 percent of the data.

Standard deviation is a measurement that can help you understand how spread out a set of numbers are.

Its useful in statistics.

Imagine if you had a survey and you asked what people thought of Answerbag from 1 to 10.
The average result was 7. [Just as an example.]

If the standard deviation is small it means everyone voted close together so almost everyone thinks Answerbag is rated approximately 7.

If the standard deviation is large it means that everyone's votes are spread out. You probably have some 1/10's and some 10/10's in there.

There is a large difference between the two, and standard deviation is simply another statical tool to help you understand the data you have.

Ok, so thats my wordy bit over.

This is what Wikipedia says:
The standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If the data points are close to the mean, then the standard deviation is small. Conversely, if many data points are far from the mean, then the standard deviation is large. If all the data values are equal, then the standard deviation is zero.
# http://en.wikipedia.org/wiki/Standard_deviation

Standard Deviation describes a distributions spread about the mean. Here is a link to a short article that briefly explains standard deviation and other descriptive statistics:
http://www.ehow.com/how_2242574_interpret-descriptive-statistics.html

Take a number of measurements. Take the average.

The standard deviation is an average deviation of a measurement from the average.

So if all the measurements are the same, the standard deviation is zero.

If the measurements are half 100mm and half 120mm, then the average is 110mm and the standard deviation is 10mm.

If the measurements are spread out, then the standard deviation gives you a measure of how spread out they are.

Strictly speaking it's the RMS average of the deviations (root of mean of squares).

G'day BoredasMustard,

Thank you for your question.

According to Wikipedia: "In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is defined as the square root of the variance.

The standard deviation is the root mean square (RMS) deviation of values from their arithmetic mean. For example, in the population {4, 8}, the mean is 6 and the standard deviation is 2. This may be written: {4, 8} ≈ 6±2. In this case 100% of the values in the population are at one standard deviation of the mean."

It shows how consistent the data is which can be used as a measure of reliability. Let's look at two students who may have the same grade point average for the year but different standard variations. Student A with the low standard variation has been consistent all year. Student B has done better than Student A in some tests and worse in others. This may indicate that Student B has had some problems during the year and if they are fixed, he or she can perform better.

I have attached sources for your reference.

Regards

Wikipedia Standard Deviation
http://en.wikipedia.org/wiki/Standard_Deviation
Standard Deviation an Introduction
http://davidmlane.com/hyperstat/A16252.html
Standard Deviation for writers and journalists
http://www.robertniles.com/stats/stdev.shtml
Wolfram Mathworld
http://mathworld.wolfram.com/StandardDeviation.html

standard deviation is how far (on average) you expect the measurement to be from the average measurement!

Standard Deviation describes a distributions spread about the mean. Here is a link to a short article that briefly explains standard deviation and other descriptive statistics:
http://www.ehow.com/how_2242574_interpret-descriptive-statistics.html