Standard Deviation Calculator
Calculate mean, variance, and standard deviation for any data set.
How this is calculated
Sample: s = sqrt(sum(x-mean)^2 / (n-1)). Population: sigma = sqrt(sum(x-mean)^2 / n).
Frequently Asked Questions About Standard Deviation Calculator
A standard deviation calculator computes statistical measures including mean (average), variance, and standard deviation for a data set. Choose between sample and population calculations.
What is standard deviation and why does it matter?
Standard deviation measures how spread out data is from the average. Low standard deviation means data points cluster near the mean, while high standard deviation means they're scattered. It's crucial in statistics for understanding data variability and making predictions.
What is the difference between sample and population standard deviation?
Population standard deviation uses n (all data points) and describes the entire population. Sample standard deviation uses n-1 and estimates the population based on a sample. Use n-1 (sample) for data that's a subset of a larger population, which is most common.
What is variance and how does it relate to standard deviation?
Variance is the average squared deviation from the mean. Standard deviation is the square root of variance, expressed in the same units as the data. Variance is used in calculations but is harder to interpret; standard deviation is more intuitive because it matches your data's scale.
What is the mean and how do I calculate it?
The mean (average) is the sum of all values divided by the count. For example, mean of [2, 4, 6, 8] = (2+4+6+8)/4 = 5. The mean is the starting point for calculating standard deviation and variance.
How do I enter data into this calculator?
Enter values separated by commas (e.g., "2, 4, 5, 8, 10"). Most calculators accept decimal numbers and handle negative values. Make sure there are no extra spaces or non-numeric characters.
What do the min and max values tell me?
Min and max show the range of your data (lowest and highest values). Combined with standard deviation, they describe your data's spread. A large range with small standard deviation suggests outliers (extreme values separate from the main cluster).