Standard Deviation
Calculate standard deviation of a data set
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Bounded Oscillatory Function: Sine and cosine oscillate smoothly between -1 and +1 with period 360° (2π rad).
Variable Mechanics
Roles, constraints & impacts
Numbers (comma-separated)
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Bounded Oscillatory Function: Sine and cosine oscillate smoothly between -1 and +1 with period 360° (2π rad).
Common Mistakes & Traps
- Using Degree mode when Radians are expected (or vice versa).
- Tangent asymptotes at 90° and 270° (division by cos θ = 0 causes undefined infinity).
- Forgetting inverse trigonometric domain limits (e.g., arcsin input must be between -1 and 1).
Dimensional Analysis & Units
Ratio of side lengths → Dimensionless Scalar [-1, +1]
Real-World & Industry Application
Audio sound wave synthesis, AC alternating current electrical waveforms, robotic arm joint kinematics, and astronomical navigation.
Worked Example: Standard Deviation
Given:
- numbers = 2, 4, 4, 4, 5, 5, 7, 9
- Mean = 5
- Variance = 4
- Standard deviation = √4 = 2
Answer: 2
Frequently Asked Questions
What is the Standard Deviation formula?
σ = √(Σ(x - μ)² ÷ n). Calculate standard deviation of a data set.
How do I calculate Standard Deviation?
Enter Numbers (comma-separated) (numbers) into the calculator. It applies σ = √(Σ(x - μ)² ÷ n) and shows every step of the working.
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