📊 Standard Deviation Calculator
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📌 Understanding Standard Deviation Calculation
Standard deviation is a measure of how spread out numbers are in a dataset. It is calculated using the formula:
- Standard Deviation (σ) = sqrt[(Σ(x – μ)²) / N]
- Where μ is the mean of the dataset, and N is the total number of values.
📌 Example Calculations
| Numbers | Standard Deviation |
|---|---|
| 10, 20, 30 | 8.16 |
| 5, 15, 25, 35 | 12.91 |
| 2, 4, 6, 8, 10 | 2.83 |
🔧 Practical Applications of Standard Deviation
1. Statistics & Data Analysis: Used to measure data dispersion in datasets.
2. Finance & Investment: Helps in analyzing stock volatility and risk assessment.
3. Quality Control: Ensures consistency in manufacturing and product analysis.
❓ FAQs
Q1: How do I calculate standard deviation?
✅ Find the mean, subtract each value from the mean, square the differences, sum them up, divide by N, and take the square root.
Q2: Can standard deviation be negative?
✅ No, standard deviation is always a positive value or zero.
Q3: Where is standard deviation commonly used?
✅ It is widely used in **finance, statistics, and quality control**.
Q4: What happens if all numbers are the same?
✅ The standard deviation will be zero, as there is no variation.
Q5: Why is standard deviation important?
✅ It helps to **measure data consistency and detect outliers in datasets**.