Online Standard Deviation Calculator
Your Free Web-based Tool for Mean, Variance, and Standard Deviation
Welcome to our free, online tool for calculating key statistical measures. This web-based calculator allows you to instantly compute the mean, variance, and standard deviation for your data set, providing both sample and population statistics without any software installation or downloads. It's an ideal solution for students, researchers, or anyone needing quick and accurate statistical analysis on any device.
Simply enter your numbers into the box below, separated by commas, spaces, or new lines. The results will appear automatically.
Results will appear here.
What is Standard Deviation?
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (average) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. It's a fundamental concept in statistics used across various fields, including finance, engineering, and quality control.
Sample vs. Population Standard Deviation
It's important to distinguish between sample standard deviation (s) and population standard deviation (σ):
- Population Standard Deviation (σ): Used when you have data for an entire population you are interested in. The calculation involves dividing the sum of squared differences from the mean by the total number of data points (N).
- Sample Standard Deviation (s): Used when you have data from a sample of a larger population. The calculation involves dividing the sum of squared differences from the mean by the number of data points minus one (n-1). This (n-1) correction, known as Bessel's correction, is used to provide a less biased estimate of the population standard deviation.
Our calculator provides both, allowing you to choose the appropriate value for your analysis.
Frequently Asked Questions
Q: What is Standard Deviation?
A: Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (average) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Q: How do I use this online standard deviation calculator?
A: Enter your numbers into the input field, separated by commas, spaces, or new lines. The calculator will automatically compute the mean, variance, and standard deviation for both sample and population data.
Q: What is the difference between sample and population standard deviation?
A: The population standard deviation (σ) is used when you have data for an entire population. The sample standard deviation (s) is used when you have data from a sample of a larger population. The formulas differ slightly, with the sample standard deviation dividing by (n-1) in the variance calculation, while the population standard deviation divides by n.
Q: What is Variance?
A: Variance is the average of the squared differences from the mean. It's a measure of how far each number in the set is from the mean. Standard deviation is simply the square root of the variance.
Q: How to calculate Standard Deviation manually?
A: 1. Find the mean of the data set. 2. Subtract the mean from each data point and square the result. 3. Find the mean of these squared differences (this is the variance). 4. Take the square root of the variance (this is the standard deviation).