Excel has two formulas for calculating the standard deviation: (1) STDEV.S and (2) STDEVP. What is the difference between them? We use STDEV.S when the mean of the population is known and STDEVP when the mean of the population is not known. In STDEV.S, the sum of squared differences from the mean is divided by ‘n-1’, whereas in STDEVP, they are divided by ‘n’. There is no difference; they are two ways of calculating the same thing. In STDEV.S, the sum of squared differences from the mean is divided by ‘n-1’, whereas in STDEVP, they are divided by ‘n-1’.
The Correct Answer and Explanation is:
Correct Answer:
In STDEV.S, the sum of squared differences from the mean is divided by ‘n-1’, whereas in STDEVP, they are divided by ‘n’.
Explanation:
In Excel, standard deviation can be calculated using several functions, but two important ones are STDEV.S and STDEVP (note that STDEVP has been replaced by STDEV.P in newer Excel versions). These two functions are used in different statistical contexts depending on whether you are analyzing a sample or the entire population.
STDEV.S is used when you are working with a sample from a larger population. In this case, you divide the sum of squared differences from the mean by n-1, where n is the number of observations. This method corrects for bias in the estimation of the population standard deviation and is called Bessel’s correction. It accounts for the fact that a sample is less variable than the population, making the estimate more accurate.
STDEVP (or STDEV.P in current Excel versions) is used when you are working with the entire population, not just a sample. Since all data points are available, there is no need to apply Bessel’s correction, so the sum of squared differences from the mean is divided by n. This gives an exact value for the population standard deviation.
The statement that STDEV.S is used when the population mean is known is incorrect. Both functions calculate standard deviation around the sample or population mean, not a separately known mean. Also, the suggestion that there is no difference between the two formulas is incorrect; the divisor in the formula (n or n-1) directly affects the result.
In summary, use STDEV.S for samples and STDEVP/STDEV.P for populations. The difference lies in the divisor: n-1 for samples, n for populations, which ensures accurate statistical analysis depending on your data set.
