1. What is Standard Deviation (σ)?

Definition: Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Purpose: It quantifies how much the individual data points differ from the mean value of the dataset.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sigma \) — Standard deviation (same units as data)
• \( x_i \) — Individual data points
• \( \mu \) — Mean of the data points
• \( n \) — Number of data points

Explanation: The calculator first computes the mean, then the squared differences from the mean, averages them (dividing by n-1 for sample standard deviation), and finally takes the square root.

3. Importance of Standard Deviation

Details: Standard deviation is crucial in statistics for understanding data variability, assessing process control, and making predictions based on data distribution.

4. Using the Calculator

Tips: Enter your data points separated by commas (e.g., "5, 10, 15, 20"). The calculator will ignore any non-numeric values.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample standard deviation?
A: Use n-1 in the denominator (as here) for sample standard deviation. For population standard deviation, divide by n instead of n-1.

Q2: What does a high standard deviation indicate?
A: High σ means data points are spread out over a wider range of values, indicating more variability.

Q3: When should I use standard deviation?
A: Use it when you need to measure dispersion in normally distributed data or compare variability between datasets.

Q4: What units does standard deviation have?
A: Standard deviation has the same units as the original data points.

Q5: How is standard deviation related to variance?
A: Variance is σ² (standard deviation squared). Standard deviation is more commonly used as it's in the original units.