Phần hướng dẫn bên dưới chưa có bằng tiếng Việt nên được hiển thị bằng tiếng Anh. Bản thân máy tính đã được dịch đầy đủ.
Cách sử dụng máy tính này
- Enter your numbers separated by commas, spaces or line breaks.
- Choose sample (most common) or population.
- Review the deviation table to see how each value contributes.
Công thức
Standard deviation measures how spread out values are around the mean. The sample formula divides by n − 1 (Bessel's correction) to give an unbiased estimate of the population variance.
Population: σ = √( Σ(x − μ)² / N )
Sample: s = √( Σ(x − x̄)² / (n − 1) )
Example
- Data: 2, 4, 4, 4, 5, 5, 7, 9; mean = 5.
- Squared deviations sum to 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32.
- Population σ = √(32/8) = 2; sample s = √(32/7) ≈ 2.138.
Câu hỏi thường gặp
What does a large standard deviation mean?
Values are spread widely around the mean. A small standard deviation means values cluster closely around it.
What is the 68–95–99.7 rule?
For roughly normal data, about 68% of values fall within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3.
Variance vs. standard deviation?
Variance is the average squared deviation; standard deviation is its square root, which has the same units as the data and is easier to interpret.