# Standard Deviation Calculator

Standard deviation (σ) calculator with mean value & variance online.

## Population and sampled standard deviation calculator

Enter data values delimited with commas (e.g: 3,2,9,4) or spaces (e.g: 3 2 9 4) and press the Calculate button.

 Enter data values: Population standard deviation: Sample standard deviation: Population variance: Sample variance: Mean:

## Discrete random variable standard deviation calculator

Enter probability or weight and data number in each row:

Probability Data number
 Standard deviation: Variance: Mean:

Here we discuss list of online math calculators that help us for doing calculation easily.

### Standard Deviation

Standard deviation is a measure of spread of numbers in a set of data from its mean value. Use our online standard deviation calculator to find the mean, variance and arithmetic standard deviation of the given numbers.Standard deviation calculator calculates the sample standard deviation from a sample:

X: x1,x2,x3,..........xn,

using simple method. It’s an online Statistics and Probability tool requires a data set (set of real numbers or valuables). The result will describe the spread of dataset, i.e. how widely it is distributed about the sample mean.

It is necessary to follow the next steps:

Enter a sample (observed values) in the box. These values must be real numbers or variables and may be separated by commas. The values can be copied from a text document or a spreadsheet.

Press the "GENERATE WORK" button to make the computation.

Standard deviation calculator will give the sample standard deviation of the sample

X: x1,x2,x3,..........xn,

standard deviation calculator gives us the stepwise procedure and insight into every step of calculation. Before the final result of sample standard deviation is derived, it calculates the arithmetic mean of a sample. The sample standard deviation calculator also calculates square of the sample standard deviation and get magnitude known as variance. These values of the sample mean and the variance can be of benefit for further solving of problems and applications.

Standard Deviation Formula

Standard deviation of a data set is the square root of the calculated variance of a set of data.

The formula for variance is the sum of the squared differences between each data point and the mean, divided by the number of data points.

When working with data from a complete population the sum of the squared differences between each data point and the mean is divided by the size of the data set, n. When working with a sample, divide by the size of the data set minus 1, n - 1.

The formula for variance for a population is:

Variance = σ2=Σ(xi−μ)2/n

Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ. Conversely, a higher standard deviation indicates a wider range of values. Similarly to other mathematical and statistical concepts, there are many different situations in which standard deviation can be used, and thus many different equations. In addition to expressing population variability, the standard deviation is also often used to measure statistical results such as the margin of error. When used in this manner, standard deviation is often called the standard error of the mean, or standard error of the estimate with regard to a mean. The calculator above computes population standard deviation and sample standard deviation, as well as confidence interval approximations.