# What is the difference between relative standard deviation and standard deviation? Can RSD and SD be negative?

Standard deviation denotes the percent of responses that fall within certain points on a bell curve, while relative standard deviation denotes the size of a standard deviation as a measure of the mean. Neither can be negative, though both can be expressed as deviations above and below the mean.

A standard deviation is a measure of how far from the mean a particular result may be. This measure is applicable to data sets that can be described as bell curve. For the bell curve, a mean is determined and results occur along a plot such that the most common result rests at the peak of the line and results above and below the mean decline simultaneously. 34.1% of results will occur within 1 standard deviation above the mean and another 34.1% of results will occur below the mean. Thus, 68.2% of results occur within 1 standard deviation from the mean. Another 27.2% of results occur within 2 standard deviations, 4.2% occur within 3 standard deviations, and 0.2% occur within 4 standard deviations.

Relative standard deviation is a transformation that allows you to determine whether a standard deviation is large or small as compared to the mean. To determine a relative standard deviation, you divide the standard deviation by the sample mean. This will allow you to determine whether the size of a standard deviation is large or small with regard to the mean of the data set. This is important because a small standard deviation might denote that all of the sample responses occurred within a narrow range, which could limit the utility of standard deviation.

Neither is expressed in terms of negative or positive. A standard deviation generally encompasses the 34.1% above and the 34.1% below the mean. Since the mean is reported, it is usually self-evident whether a particular value is above or below the mean, so only the number (or fraction of a number) of the standard deviation is necessary.

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