Standard Deviation Calculator
Calculate standard deviation, variance, mean, median, mode, and other descriptive statistics from your dataset.
Standard Deviation Calculator
Calculate standard deviation, variance, mean, median, mode, and other statistics
Separate numbers with commas, spaces, or new lines
Formula
σ = √(Σ(x - μ)² / N) or s = √(Σ(x - x̄)² / (n-1))Population standard deviation (σ) divides by N, while sample standard deviation (s) divides by n-1 (Bessel's correction).
Understanding Standard Deviation
Low Standard Deviation
Data points are clustered close to the mean. The values are consistent and predictable.
Example: Test scores of 88, 90, 91, 89, 92
Medium Standard Deviation
Data points show moderate spread around the mean. Some variation is present.
Example: Test scores of 75, 85, 90, 95, 80
High Standard Deviation
Data points are spread far from the mean. High variability in the dataset.
Example: Test scores of 50, 70, 90, 100, 65
How to Use
- 1Enter your data — Input your numbers separated by commas, spaces, or new lines.
- 2Calculate — Click Calculate to compute all statistics.
- 3View results — See standard deviation, variance, mean, median, mode, and more.
- 4Choose the right measure — Use sample statistics for samples, population statistics for complete datasets.
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means data points are close to the mean, while a high standard deviation means they are spread out.
What is the difference between sample and population standard deviation?
Sample standard deviation (s) uses n-1 in the denominator (Bessel's correction) and is used when your data is a sample from a larger population. Population standard deviation (σ) uses n and is used when you have data for the entire population.
What is variance?
Variance is the square of the standard deviation. It measures the average squared deviation from the mean. Standard deviation is often preferred because it's in the same units as the original data.
What is the difference between mean, median, and mode?
Mean is the arithmetic average. Median is the middle value when data is sorted. Mode is the most frequently occurring value. Each measures central tendency differently and is useful in different situations.
When should I use median instead of mean?
Use median when your data has outliers or is skewed. The median is more robust to extreme values. For example, median income is often more representative than mean income because a few very high incomes can skew the mean.