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标准差计算器

计算数据集的标准差和方差。

While the average (mean) tells you where the center of your data is, the Standard Deviation tells you how spread out the numbers are. In fields like finance, science, and quality control, understanding this 'volatility' or 'dispersion' is just as important as knowing the average. A low standard deviation indicates that the data points tend to be very close to the mean, suggesting consistency. A high standard deviation indicates that the data points are spread out over a wider range, suggesting higher variability or risk. Our calculator provides both the Standard Deviation and the Variance, giving you a complete picture of your data's distribution.

标准差

5.2372

Standard Deviation: 5.2372 (Count: 8)

Numbers10, 12, 23, 23, 16, 23, 21, 16
个数8
平均值18.0000
方差27.4286

工作原理

This tool calculates the Mean of your data, then finds the difference between each data point and that Mean. It squares those differences (to ensure they are positive), averages them to find the Variance, and finally takes the square root of that result to provide the Standard Deviation.

计算公式

σ = √(Σ(x - μ)² / n)

Calculation Examples

For the data set [10, 20, 30]: 1. **Mean**: 20 2. **Variance**: ((10-20)² + (20-20)² + (30-20)²) / 3 = **66.67** 3. **Standard Deviation**: √66.67 ≈ **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.

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