Standard Deviation Calculator

A Standard Deviation Calculator is an online tool that quickly computes the standard deviation of a dataset, saving time and reducing manual calculation errors. It is useful for students, analysts, and researchers who need accurate results for statistical analysis. The calculator supports both population and sample data, offering flexibility for different applications. By simplifying complex formulas, a Standard Deviation Calculator helps users understand data dispersion, compare datasets, and make informed decisions based on variability.

What is Standard Deviation?

Standard deviation (SD) is a statistical measure that tells you how spread out your data values are from the mean.

• A low standard deviation means the values are close to the mean.
• A high standard deviation means the values are widely spread out.

The mathematical definition for standard deviation (σ) is the positive square root of the variance (σ²).

$$\text{variance =}{\sigma }^2$$ $$\text{standard deviation =}\sqrt{{\sigma }^2}=\sigma$$

Standard Deviation Formula

Standard Deviation can be calculated in two ways, depending on the type of dataset you have.

Population Standard Deviation Formula

$$\sigma =\sqrt{\frac{\sum _{}^{}{(x_i-\mu )}^2}{N}}$$

Where:

• $\sigma$ = population standard deviation
• $x_i$ = each data point
• $\mu$ = population mean
• $N$ = total number of values

Sample Standard Deviation Formula

$$s=\sqrt{\frac{\sum _{}^{}{(x_i-\bar{x})}^2}{n-1}}$$

Where:

• $s$ = sample standard deviation
• $x_i$ = each data point
• $\bar{x}$ = sample mean
• $n$ = number of sample values
• $n-1$ = degrees of freedom

How to Find the Variance Using Our Calculator?

• Enter the values separated by a comma, a space, or a new line.
• Click “Calculate” and the tool automatically computes Mean, Population Standard Deviation, and Sample Standard Deviation.