मानक विचलन कैलकुलेटर — सूत्र
## How to Calculate Standard Deviation
### Formula (Population)
**σ = √[ Σ(xᵢ - μ)² / N ]**
### Steps
1. Find the mean (μ) of the data set
2. Subtract the mean from each value and square the result
3. Find the average of those squared differences
4. Take the square root
For a **sample** standard deviation, divide by (N-1) instead of N.
### Formula (Population)
**σ = √[ Σ(xᵢ - μ)² / N ]**
### Steps
1. Find the mean (μ) of the data set
2. Subtract the mean from each value and square the result
3. Find the average of those squared differences
4. Take the square root
For a **sample** standard deviation, divide by (N-1) instead of N.
हल किया गया उदाहरण
Find the standard deviation of 10, 20, and 30.
- Mean = (10 + 20 + 30) / 3 = 20
- Squared differences: (10-20)² = 100, (20-20)² = 0, (30-20)² = 100
- Variance (population) = (100 + 0 + 100) / 3 = 66.6667
- Standard Deviation = √66.6667 ≈ 8.1650