Tabla de Contenidos
The standard deviation is a statistical parameter that allows evaluating the dispersion of a set of values. If the average of a set of values is calculated, the standard deviation evaluates the difference of the values in the set from the average. Remember that the average (or mean) of a set of values is the sum of all of them divided by the number of values we have. The relative standard deviation is the ratio of the standard deviation to the average of the set of values; It gives an idea of the dispersion of the values with respect to the values themselves . Let’s see how it is calculated.
The standard deviation σ is calculated with the following formula:
Expressed in words: if we have a set with n values, we subtract from each value of the set that we analyze, which we denote with the subscript i , the average of all the values. We square each of these differences and add them, to then divide the result by the number of values in the set n minus 1 ( n – 1), and calculate the square root of this value.
Samples and populations
The standard deviation has two different definitions, depending on the type of data we are analyzing. This difference implies a slightly different calculation.
The standard deviation can be calculated on an entire population or on a sample of a population. If data is collected from all members of a population or a set, the standard deviation of a population must be used. If you are analyzing data that represents a sample from a larger population, you must use the standard deviation of a sample.
The difference in the calculation is that, in the case of the standard deviation of a sample, the difference between each value and the squared average is divided by the number of values minus 1 ( n – 1), as we see in the figure . For the standard deviation of a population, divide by n .
The relative standard deviation
As already said, the average of a set of values, which we will now call p , is the sum of all of them divided by the number of values n . Following the previous definition, the relative standard deviation σ r is calculated with the following formula
σr = σ/ p
The relative standard deviation σ r is usually expressed as a percentage of the average p ; in that case the formula takes the following form
σr = ( σ x 100)/ p
Sources
- Yadolah Dodge. The Concise Encyclopaedia of Statistics . New York: Springer, 2010.
- Padgalskas, V. How to Calculate Relative Deviation . Geniusland.com, 2018.
