What does a high standard deviation mean?

It means the data points are spread far from the mean, indicating high variability or volatility in your dataset.

Standard Deviation Calculator – Measure Variance | CalcTools

Calculate standard deviation and variance for any dataset. Understand the volatility and spread of your data.

The average tells you where your data is centered, but the Standard Deviation tells you how reliable that center is. In finance, standard deviation is the primary measure of risk and volatility; in manufacturing, it is the key to quality control. Our Variance and Standard Deviation service helps you quantify the 'spread' of your information, letting you know if your data points are tightly clustered or widely scattered. This is a vital service for anyone who needs to measure the consistency or uncertainty of their results.

Data Points

Standard Deviation (σ)

5.2372

Standard Deviation: 5.2372 (Count: 8)

Numbers10, 12, 23, 23, 16, 23, 21, 16

Count8

Mean18.0000

Variance (σ²)27.4286

How it Works

This tool calculates the mean, finds the squared difference of each point from that mean, averages those differences to find the Variance, and finally takes the square root to provide the Standard Deviation.

Calculation Formula

σ = √(Σ(x - μ)² / n)

Calculation Examples

For [10, 20, 30]: Mean=20, Variance=**66.67**, Std Dev=**8.16**.

Why use this tool in your daily life?

Knowledge of variance is knowledge of risk. This service is essential for traders, scientists, and engineers who need to understand the margins of error and the reliability of their systems.