Sample & Population Standard Deviation Difference & Usages

The below short notes may useful to understand the difference between sample & population standard deviation and to know where to use sample & population standard deviation method.

Difference between sample & population SD

Standard deviation in statistics is one of the important aspects in statistics to analyze the statistical data to determine the data dispersion from the expected value. For beginners who started analyzing statistical data using this method, it is very obvious to get stumbled to determine which method either sample standard deviation or population standard deviation to be used to find the data dispersion of the experimental data. The main difference is the sample SD is calculated from the random samples of the population and population SD is calculated from entire population data.

Where to use sample or population standard deviation

In general, either one of these two methods can be used to find the dispersion or deviation value from the mean or expected value but the selection of method mainly depends on the availability of data. The experiment is provided with entire population data then the population standard deviation using N formula method can be used to determine the data dispersion from the population mean. The formula to determine the data dispersion value of entire population data is

where
σ is the population SD
N is the total number of sample data impulses
x_{i} is the data impulse
x̄ is the mean or expected value of sample data

However, getting the entire population data is not possible for every experiment. In such instances the sample standard deviation method can be used to estimate the data dispersion of the random samples of the population data from the sample mean. It's one of the most popular methods being used in statistical data analysis using the (N-1) formula method. The formula to estimate the random samples dispersion or deviation from the sample mean can be calculated from

where
σ_{N} is the population SD
N is the total number of data impulses
x_{i} is the data impulse
x̄ is the mean or expected value of entire population

In normal distribution, the standard deviation is a Bell shaped curve and the 68.27%, 95.45% and 99.73% of data spread across 1σ, 2σ and 3σ respectively. The lesser dispersion value from mean provides better results or provides more accuracy for the experiments. The larger dispersion value will have more error in the experiment. Many experiments such as measuring risk of investments (stocks, bonds, mutual funds, etc.) in finance, forecasting the weather, digital & analog signal processing, product pricing, telecommunication, polling etc. requires standard deviation to perform the statistical data analysis. These featured tools sample standard deviation calculator & population standard deviation calculator may be used to estimate or determine the data dispersion from mean.