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Start with the basic understanding of what standard deviation is. Standard deviation is a mathematical concept used in statistics to quantify the amount of variation or dispersion in a data set. This variation tells how far each value in the set is from the mean, or average, value.

In second step, we consider the mathematical formula for standard deviation. In this formula, each data point in the set is subtracted from the mean, then squared. This makes all the resulting values positive (because the square of any real number, whether positive or negative, is always positive). These squared deviations are then averaged and the square root is taken, yielding the standard deviation. Here's the formula: \[ \(\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}\) \] Where: - \(\sigma\) is the standard deviation, - \(N\) is the number of data points, - \(x_i\) is each individual data point, and - \(\mu\) is the mean of the data set.

Given its mathematical definition, it's clear that standard deviation cannot be negative. The sum of squares in the formula guarantees that the result under the square root sign will always be positive or zero, because squares of real numbers are never negative. Thus, taking the square root of a positive number or zero results in another positive number or zero.