What is statistical standard deviation?

Question

What is statistical standard deviation of some set of values? I am not a mathematician. Can you give me some simple example or explain it to me in simple terms?

Answer 1

lets use data that has been well established, IQ.
IQ has a mean (average) = to 100. The standard deviation is 15.
What standard deviation is, "is the average of how each score in the sample varies from the mean score or average."
It has been established through sampling that IQ mean =100 and standard deviaation =15 . So on average, each score varies from the mean by 15 for this data. It could be more or could be less though.
The sample data from IQ is what is known as "normally distributed" (the bell curve) . The bell curve is a probability distribution, therefore data can be extrapolated. For example, 68 percent of IQ scores fall within 1 standard deviation of the mean.
therefore 68 percent of IQ scores will range from 85 to 115.
95 percent of the scores be 2 standard deviations from the mean. scores range from 70 to 130 will account for 95 percent of the scores. Nearly all scores will be within 3 standard deviations of the mean 55 to 145.
Please note that there are IQ scores below 55 and above 145 though that is very rare.
check out a Z table (google Z table) which shows the probability distribution

Answer 2

The area under a normal curve such as the 'bell' curve used to represent human IQ, where 100 is average by definition, can be divided by vertical lines at intervals of one 'standard deviation' for evaluation. For example most of the population fall within plus or minus one standard deviation. The area within plus or minus two standard deviations represents the vast majority of people. Exceptional individuals with very high or very low IQ's fall within the ares represented by the third standard deviation interval on either side of the middle. A particular individuals IQ may be at a interval such as plus 1.2 standard deviations on the chart. Deviation means a difference from some reference (the middle) and a standard deviation is a particular repeatable interval that can be readily calculated from statistical data (when there is enough data to represent the population). Standard deviations can refer to any population (heights of people, lengths of machined parts, weights of rabbits, etc.) under investigation.

Answer 3

See my answer to a question about six hours ago which asked for explanation of standard deviation and correlation.