Sample Standard Deviation Calculator
Sample standard deviation measures data spread from the mean in a dataset. It's crucial in statistics for understanding data variability, assessing investment risks, quality control, and scientific research. This calculator helps students, researchers, and professionals quickly compute standard deviation while learning the underlying methodology.
Formula
s = √[Σ(xᵢ - x̄)²/(n - 1)]
Where:
s = sample standard deviation
x̄ = sample mean
n = number of data points
How to Use
1. Enter numbers separated by commas in the input field
2. Click "Calculate" to get results
3. View step-by-step calculation process
4. See standard deviation value
5. Click "Clear" to reset all fields
Calculation Process
FAQs
1. Why use sample standard deviation instead of population?
Sample standard deviation (n-1) is used when working with a subset of data to reduce bias. Population standard deviation (N) uses complete data. The n-1 correction (Bessel's correction) provides better estimation for larger populations from small samples.
2. What's the difference between variance and standard deviation?
Variance is the average squared deviation from the mean, while standard deviation is its square root. Standard deviation shares the same units as original data, making it more interpretable for spread measurement.
3. Can standard deviation be negative?
No. Since it's derived from squared differences, standard deviation is always non-negative. A value of 0 indicates all values are identical.
4. How does outlier affect standard deviation?
Outliers significantly increase standard deviation as they increase the average distance from the mean. It's more sensitive to outliers than mean absolute deviation.
5. When should I use sample standard deviation?
Use sample standard deviation when analyzing a representative subset of a larger population. For complete population data, use population standard deviation formula (divide by N instead of n-1).