The concept of the standard deviation has a number of practical applications within a range of research projects. In a broad sense, the concept of standard deviation allows a researcher to define a realm of expected normal variation. When one is investigating either the natural or the human world, there is almost always a range of possible answers for any given question. In more purely mathematical terms, the standard deviation permits a researcher to measure the range of values of a set of numbers (which correlate to a set of research results) by using a particular way of measuring the expected range or spread of the majority of answers or responses (in the case of standard deviation the variation in a distribution is defined equaling the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.
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