chener said:The standard deviation is defined by:
http://www.mathsisfun.com/data/standard-deviation-formulas.html
The formula for calculating the standard deviation of a Gaussian distribution is:
The standard deviation is a measure of how spread out the data points are from the mean in a Gaussian distribution. A larger standard deviation indicates a wider spread of data points, resulting in a flatter and wider-shaped curve. Conversely, a smaller standard deviation indicates a tighter spread of data points, resulting in a taller and narrower-shaped curve.
No, the standard deviation of a Gaussian distribution cannot be negative. It is always a positive value, as it represents the distance from the mean. If the standard deviation were to be negative, it would imply that some data points are located to the left of the mean, which is not possible for a Gaussian distribution.
Changing the standard deviation directly affects the shape of a Gaussian distribution. A larger standard deviation results in a wider and flatter curve, while a smaller standard deviation results in a narrower and taller curve. The standard deviation also determines the spread of data points and the likelihood of obtaining a certain value from the distribution.
No, the standard deviation and variance in a Gaussian distribution are not the same. The variance is calculated by squaring the standard deviation, and it represents the average squared distance from the mean. While the standard deviation is measured in the same units as the data, the variance is measured in squared units, making it less interpretable compared to the standard deviation.