1. What is Standard Deviation?

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It shows how much variation exists from the average (mean) value.

2. How Does the Calculator Work?

The calculator uses the standard deviation formula:

Where:

• \( \sum x^2 \) — Sum of squared values
• \( n \) — Sample size
• \( \bar{x} \) — Mean of the values
• \( \sqrt{\frac{n}{n-1}} \) — Bessel's correction for sample standard deviation

Explanation: The equation calculates how spread out numbers are from their mean value, with correction for sample bias.

3. Importance of Standard Deviation

Details: Standard deviation is crucial in statistics for measuring variability, assessing process quality, and understanding data distribution.

4. Using the Calculator

Tips: Enter the sum of squared values, the mean, and sample size (n ≥ 2). All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample standard deviation?
A: Sample standard deviation includes Bessel's correction (n-1) to account for sampling bias, while population standard deviation uses n.

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

Q3: When should I use this formula?
A: Use this when you have the sum of squares and mean, but not the original data points.

Q4: What are common standard deviation values?
A: In normal distributions, about 68% of values fall within ±1σ, 95% within ±2σ, and 99.7% within ±3σ.

Q5: Can standard deviation be negative?
A: No, standard deviation is always non-negative as it's derived from squared differences.