Before learning the sample standard deviation formula, let us see when do we use it. In a practical situation, when the population size N is large it becomes difficult to obtain value xi for every observation in the population and hence it becomes difficult to calculate the standard deviation (or variance) for the population. In such cases, we can estimate the standard deviation by calculating it on a sample of size n taken from the population of size N. This estimated variance is called the sample standard deviation(S). Let us explore the sample standard deviation formula below.
What Is the Sample Standard Deviation Formula?
There are two types of standard deviations, population standard deviation and sample standard deviation. Given a sample of data (observations) for the random variable x, its sample standard deviation formula is given by