1. What is Sample Standard Deviation?

The sample standard deviation (s) measures the dispersion of data points in a sample relative to their mean. It's the square root of the sample variance and indicates how spread out the values are.

2. How Does the Calculator Work?

The calculator uses the sample standard deviation formula:

Where:

• \( s \) — Sample standard deviation
• \( x \) — Individual data points
• \( \bar{x} \) — Sample mean
• \( n \) — Sample size

Explanation: The formula calculates the square root of the average squared deviations from the mean, using n-1 (Bessel's correction) for unbiased estimation.

3. Importance of Standard Deviation

Details: Standard deviation is crucial in statistics for measuring variability. It's used in hypothesis testing, confidence intervals, quality control, and risk assessment.

4. Using the Calculator

Tips: Enter numeric values separated by commas (e.g., 5, 8, 12, 6, 9). At least two values are required. Non-numeric entries will be ignored.

5. Frequently Asked Questions (FAQ)

Q1: Why use n-1 instead of n in the denominator?
A: Using n-1 (Bessel's correction) provides an unbiased estimate of the population standard deviation from a sample.

Q2: What's the difference between sample and population standard deviation?
A: Population standard deviation uses n in the denominator and is used when you have all data points. Sample standard deviation uses n-1 for samples.

Q3: When should I use standard deviation?
A: Use it when you need to measure dispersion in normally distributed data. For skewed distributions, consider interquartile range.

Q4: What does a high standard deviation indicate?
A: High standard deviation means data points are spread out widely from the mean, indicating high variability.

Q5: How is standard deviation related to variance?
A: Standard deviation is the square root of variance. SD has the same units as the original data, making it more interpretable.