Calculate variance and standard deviation for population or sample data instantly.
This tool calculates the standard deviation of a data set โ a measure of how spread out the values are from the mean (average). It's a fundamental statistic used in research, finance, quality control, and any field analyzing data variability.
Standard Deviation (ฯ) = โ(ฮฃ(x โ mean)ยฒ รท N), where x is each data point, mean is the average of all values, and N is the number of data points (or Nโ1 for sample standard deviation, which corrects for bias when working with a sample rather than an entire population).
Enter your list of numbers, and the calculator returns the mean, variance, and standard deviation, typically offering both population and sample calculation options.
Example: For the data set 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5, and the population standard deviation is 2, meaning most values fall within about 2 units of the average.
What's the difference between population and sample standard deviation? Population standard deviation divides by N (the full data set size), used when you have data for an entire population; sample standard deviation divides by Nโ1, which corrects for bias when your data is only a sample representing a larger population.
What does a low standard deviation mean? A low standard deviation means data points are clustered closely around the mean, indicating more consistency; a high standard deviation means data points are more spread out and variable.
How is standard deviation different from variance? Variance is the average squared deviation from the mean, while standard deviation is the square root of variance โ standard deviation is more commonly used because it's expressed in the same units as the original data, making it easier to interpret.
Why is standard deviation important in finance? It's commonly used to measure investment volatility or risk โ a higher standard deviation in returns indicates greater price fluctuation and risk compared to a lower standard deviation.
What percentage of data falls within one standard deviation of the mean? In a normal (bell curve) distribution, approximately 68% of data falls within one standard deviation of the mean, about 95% within two, and about 99.7% within three โ known as the empirical rule.