Standard Deviation Calculator
Calculate mean, sum, variance, standard deviation, and margin of error for population or sample data.
What Is Standard Deviation?
Standard deviation is a measure of how much the values in a data set vary from the mean. A lower standard deviation indicates that the values are closer to the mean, while a higher standard deviation indicates greater variation.
This calculator can calculate the mean, variance, standard deviation, and margin of error for both population and sample data.
Population Standard Deviation
Population standard deviation is used when the entire population is being measured. It is calculated using the number of values in the complete data set.
The population standard deviation is the square root of the population variance.
Sample Standard Deviation
Sample standard deviation is used when the data represents a sample of a larger population. The corrected sample calculation uses the sample size minus one.
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how much values in a data set vary from the mean.
What is the difference between population and sample standard deviation?
Population standard deviation is used when the entire population is being measured. Sample standard deviation is used when the data represents a sample of a larger population.
How should I enter the numbers?
Enter the values separated by commas. For example: 12, 18, 15, 21, 16.
What does a high standard deviation mean?
A higher standard deviation generally means that the values are more spread out from the mean.
What is the margin of error?
The margin of error estimates how much the sample statistic may differ from the true population value. This calculator uses a 95% confidence level to calculate the margin of error.
Disclaimer
This calculator is provided for general mathematical, educational, and statistical purposes. While we aim to provide accurate results, SmartMyTools does not guarantee that the results are suitable for professional, academic, scientific, statistical, or other specialized applications. The margin of error is an estimate based on the calculator's selected calculation method and should not be considered a substitute for professional statistical analysis.