How to Calculate Sample Deviation

Sample Standard Deviation Formula:

\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n - 1}} \]

Sample Size (n):

Mean (Average):

Sample Standard Deviation:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Sample Standard Deviation?

Sample Standard Deviation measures the amount of variation or dispersion in a set of sample data values. It indicates how spread out the data points are from the mean (average) value.

2. How Does the Calculator Work?

The calculator uses the sample standard deviation formula:

\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n - 1}} \]

Where:

\( s \) — Sample standard deviation
\( x_i \) — Individual data points
\( \bar{x} \) — Mean (average) of the data points
\( n \) — Sample size (number of data points)
\( \sum \) — Summation symbol

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

3. Importance of Sample Standard Deviation

Details: Sample standard deviation is crucial in statistics for understanding data variability, assessing reliability of results, and making inferences about populations from samples. It's widely used in research, quality control, and data analysis.

4. Using the Calculator

Tips: Enter your data points separated by commas (e.g., "2,4,6,8,10"). The calculator will compute the sample size, mean, and sample standard deviation. Minimum 2 data points required.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sample and population standard deviation?
A: Sample SD uses n-1 (Bessel's correction) for unbiased estimation, while population SD uses N. Sample SD estimates population variability from a subset.

Q2: Why use n-1 instead of n in the denominator?
A: Using n-1 corrects for bias when estimating population variance from a sample, providing an unbiased estimator (Bessel's correction).

Q3: When should I use sample standard deviation?
A: Use sample SD when working with a subset of data representing a larger population. Use population SD when you have data for the entire population.

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

Q5: Can standard deviation be negative?
A: No, standard deviation cannot be negative as it's derived from squared differences and square roots, always resulting in non-negative values.