To calculate the relative standard deviation, divide the standard deviation by the mean and then multiply the result by 100 to express it as a percentage. The relative standard deviation is also known as the coefficient of variation or the variation coefficient. Engineers and researchers use it to determine precision and repeatability in data that they gather from their experiments.
- Write the equation
Write the formula for the relative standard deviation as a percentage. It is RSD = (SD/Xbar) * 100, where SD is the standard deviation and Xbar is the mean.
- Find the mean
Perform the calculation for the mean, which is also called the average. The equation is Xbar = Xsum/N, where Xsum is the sum of all the data points, and N is the total number of points. For a data set consisting of points 1, 3, 3 and 5 write Xbar = (1 + 3 + 3 + 5)/4 = 12/4 = 3.
- Calculate the standard deviation
Solve for the standard deviation, which is the square root of the average of the square differences of each point minus the mean. Consider the points 1, 3, 3 and 5, where the mean is Xbar = 3. The standard deviation is Square root [((1-3)^2 + (3-3)^2 + (3-3)^2 + (5-3)^2)/4] = Square root [(-2)^2 + 0 + 0 + 2^2)/4] = Square root (8/4) = Square root (2) = 1.4.
- Compute the relative standard deviation
Plug the standard deviation and mean values into the formula, and do the math. For points 1, 3, 3, and 5 where the mean is 3 and the standard deviation is 1.4, RSD = (1.4/3)*100 = 46.67%.