*Standard Deviation Calculator* is an online statistics and probability tool for data analysis programmed to calculate common measure of the spread of a data set. This calculator computes the output values of SD, Population SD, SD Variance and PSD Variance of a given input values of data set

### Definition

The **standard deviation** is a common measure of the spread of a data set or distribution and broadly used in statistics and probability theory for the assessment of variability or diversity employed. It explains how much variation or **dispersion** from the average mean, or expected value. A low SD shows that the data points tend to be very close to the mean, whereas high SD shows that the data are spread out in excess of a large range of values. When it comes to statistical theory standard deviation calculation is more important and highly in demand. The square root of the variance is called the Standard Deviation, usually denoted by **s**. It is often abbreviated to **SD**. The variance is calculated from the squares of the observations

### Formulas

Standard Deviation can be calculated from the below formula

The formula to calculate Population SD is:

The formula to calculate Variance is:

The formula to calculate Mean is:

The **mean** is a measure of central tendency value for a distribution, is the same as the average of the data set. It's also popularly known as **arithmetic mean** or **average** often referenced along with the standard deviation; which describes the central location of the data and the SD describes the spread. Central limit theorem states that regardless of the data set and approach a normal distribution when the data set is large. Most of the calculations made regarding normal distribution therefore, the normal distribution is important in statistics

The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand theory of Probability and Statistics. The set of ideas which is intended to offer the way for making scientific implication from such resulting summarized data. In many applications it is necessary to calculate the Standard Deviation, PSD, SD Variance and PSD Variance for a given set of data. When it comes to online calculation, this Standard Deviation calculator can help you to effortlessly make your calculations for a given data set