Standard Deviation
Standard deviation measures how spread out data values are from the mean. It is the most widely used measure of statistical variability, appearing in quality control, finance (portfolio volatility), scientific research, and machine learning. Our calculator handles both population and sample standard deviation, shows the full variance table, and visualizes the distribution.
أرقام (مفصولة بفاصلة أو مسافة)
الانحراف المعياري للعينة (s)
Population Std Dev (σ)
المتوسط
التباين
حول Standard Deviation Calculator
Standard deviation measures how spread out data values are from the mean. It is the most widely used measure of statistical variability, appearing in quality control, finance (portfolio volatility), scientific research, and machine learning. Our calculator handles both population and sample standard deviation, shows the full variance table, and visualizes the distribution.
كيفية الاستخدام
- Enter your data values separated by commas or line breaks.
- Choose population (σ) or sample (s) standard deviation.
- See mean, median, variance, standard deviation, and range.
- View the frequency distribution and normal curve overlay.
الصيغة والمنهجية
Mean: μ = Σx / n. Population variance: σ² = Σ(x−μ)² / n. Sample variance: s² = Σ(x−μ)² / (n−1). Standard deviation = √variance. The n−1 denominator (Bessel's correction) makes the sample variance an unbiased estimator of the population variance.
حالات الاستخدام الشائعة
- Finance: measuring stock volatility (higher σ = higher risk)
- Quality control: Six Sigma (process within ±3σ = 99.73% conformance)
- Academic grading: normalizing test scores to a curve
- Scientific experiments: reporting measurement uncertainty
- A/B testing: determining statistical significance of results
الأسئلة الشائعة
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