Choose Population or Sample
Enter a list of numbers separated by commas, spaces, and/or line breaks to find the standard deviation. The calculator will automatically remove invalid values (such as letters, words, and symbols).
How to Use The Standard Deviation Calculator
To use this standard deviation calculator, begin by specifying whether your data represents an entire
population or a
sample. Select either option in the drop-down menu.
Next, delete the default data example and enter your data.
Your data set should be separated by commas:
1 5.8 -50.98 18926 7509.6506832
or line breaks:
or a combination of commas, spaces, and line breaks:
What is Standard Deviation
Standard Deviation, most commonly expressed as σ, is a measure of the variation of values in a data set.
A low standard deviation means the values in a data set tend to be close to the mean, while a higher standard deviation indicates that the values are spread out over a wider range.
Population vs Sample
While the goal of calculating standard deviation is always to represent the variation in data for an entire population, we're often only presented with a sample of data.
When only given a sample of data, the standard deviation of a population can be estimated from a sample standard deviation.
How to Calculate Standard Deviation
Standard deviation is calculated by finding the square root of a data set's variance.
When a data set represents an entire population, the population variance is the sum of the squared differences between each data point and the mean (sum of squares), divided by the count of the data set (n). Population standard deviation is the square root of the population variance.
If instead we only have a sample of data from the population, sample variance is calculated by finding the sum of the squared differences between each data point and the mean, then dividing it by the count minus one (n-1). Sample variance is the square root of the sample variance.