Sample Standard Deviation Formula Calculator

Sample Standard Deviation Formula:

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

Sample Standard Deviation (s):

Mean (x̄):

Sample Size (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Sample Standard Deviation?

The sample standard deviation (s) measures the dispersion or spread of a set of data points. It quantifies how much the individual data points differ from the mean (average) value of the sample.

2. How Does the Calculator Work?

The calculator uses the sample standard deviation formula:

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

Where:

\( s \) — Sample standard deviation
\( x_i \) — Individual data points
\( \bar{x} \) — Sample mean (average)
\( n \) — Sample size
\( \sum \) — Sum of all values

Explanation: The formula calculates the square root of the average squared deviation of each data point from the mean, with a correction factor (n-1) for sample data.

3. Importance of Standard Deviation

Details: Standard deviation is crucial in statistics for understanding data variability. A low standard deviation indicates data points are close to the mean, while a high standard deviation indicates data are spread out over a wider range.

4. Using the Calculator

Tips: Enter your numerical values separated by commas (e.g., 5, 8, 12, 6, 9). The calculator will compute the mean, sample size, and standard deviation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample standard deviation?
A: Population standard deviation divides by N, while sample standard deviation divides by N-1 (Bessel's correction) to account for sampling variability.

Q2: When should I use sample standard deviation?
A: Use sample standard deviation when your data represents a sample from a larger population. Use population standard deviation if you have all possible data points.

Q3: What does a standard deviation of zero mean?
A: A standard deviation of zero indicates all values in the dataset are identical (no variability).

Q4: How is standard deviation related to variance?
A: Variance is the square of standard deviation. Standard deviation is in the original units, making it more interpretable.

Q5: What's a "good" standard deviation?
A: There's no universal "good" value - it depends on context. Compare it to the mean (coefficient of variation = SD/mean) to assess relative variability.