Calculate sample and population standard deviation of a data set with this online calculator. Find statistical dispersion. Use a dot as the decimal separator.
Sample Standard Deviation (s)
Population Standard Deviation (σ)
Standard deviation is a statistical measure that quantifies the dispersion or variability of a data set relative to its statistical mean. Essentially, standard deviation indicates how far individual values are from the average of the data set.
In simpler terms, if all the data in a set are very similar to each other, the standard deviation will be low, indicating little dispersion. Conversely, if the data vary significantly, the standard deviation will be high, signaling greater dispersion.
There are two main types of standard deviation used in statistics to measure data dispersion: sample standard deviation and population standard deviation. Each applies in different contexts depending on whether you are working with a sample or a complete population.
Sample standard deviation is used when you have a sample of data rather than the entire population. It is calculated by taking the square root of the sample variance, which is obtained by dividing the sum of the squared differences between each data point and the sample mean by the number of data points in the sample minus one (n-1). This adjustment, known as Bessel’s correction, helps to obtain a more accurate estimate of the population standard deviation from a sample.
Population standard deviation is used when you have data for the entire population. It is calculated by taking the square root of the population variance, which is obtained by dividing the sum of the squared differences between each data point and the population mean by the total number of data points in the population (N). This formula provides an exact measure of dispersion in the context of the entire population without additional adjustments.
To calculate standard deviation, first you need to find the statistical mean of your data. Then, subtract the calculated mean from each individual value, square the result, and sum these squares. If you are working with a sample, divide the sum of squares by the total number of data points minus one (n-1) to obtain the sample variance. If you are working with the entire population, divide by the total number of data points (N) to obtain the population variance. Finally, take the square root of the variance to get the standard deviation.
Where:
Where:
The statistical mean x is calculated by summing all the sample values and dividing by the total number of data points.
Where:
The main difference between standard deviation and variance lies in how they measure data dispersion. Variance quantifies dispersion by calculating the average of the squared differences between each data point and the mean, resulting in a measure in squared units. In contrast, standard deviation is the square root of the variance, returning the dispersion measure to the same units as the original data.