Laboratory Formula
Sample Standard Deviation Formula
Measures the spread of sample observations around their mean.
Formula Summary
Sample Standard Deviation
Measures the spread of sample observations around their mean.
- Category
- Laboratory
- Equation
- s = √(Σ(xᵢ − x̄)² ÷ (n − 1))
- Calculator
- Use Sample Standard Deviation Calculator →
Equation
s = √(Σ(xᵢ − x̄)² ÷ (n − 1))
Variables
- s = sample standard deviation
- xᵢ = each value
- x̄ = sample mean
- n = sample size
How to Use This Formula
- Identify the known values from the problem statement.
- Convert all values into compatible units.
- Substitute the values into the equation and calculate the result.
- Check that the final answer has the correct unit and meaning.
Explanation
Sample standard deviation measures how spread out a set of sample measurements are around their average value. It helps describe the variability and consistency of experimental data.
Worked Example
For sample values 4, 6, and 8, the standard deviation shows how much the measurements vary from their mean value of 6.
Common Mistakes
- Using population standard deviation when working with a sample.
- Dividing by n instead of n − 1 for sample data.
- Calculating deviations from the wrong mean value.
Applications
- Analyzing experimental measurement variation.
- Evaluating precision of laboratory results.
- Studying reliability of collected data.
Related Formulas
Percent Error
% error = |experimental − accepted| ÷ |accepted| × 100
Compares an experimental result with an accepted reference value.
Learn formula →Percent Difference
% difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
Compares two experimental values when neither is an accepted value.
Learn formula →Coefficient of Variation
CV = s ÷ x̄ × 100
Expresses variability relative to the mean as a percentage.
Learn formula →