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Standard Deviation Calculator.

Calculate population and sample standard deviation with variance

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Set your values

Results update as you type.

Sample Results

Mean (μ)18.0000
Variance (s²)27.4286
Standard Deviation (s)5.2372

Results

Count (n)8
Sum (Σx)144.00
Median18.5000
Mode23
Range13.00
Minimum / Maximum10 / 23

Sorted Data

10, 12, 16, 16, 21, 23, 23, 23

Understanding Standard Deviation

Interpretation: A low standard deviation means data points are close to the mean. A high standard deviation means data is spread out over a wider range.
Population vs. Sample: Population Standard Deviation (σ): Use when you have data for the entire population. Divides by N. Sample Standard Deviation (s): Use when you have a sample of a larger population. Divides by N-1 (Bessel's correction).

Cite this calculator

Canonical URL: https://mathify.one/zh/math/standard-deviation

Cite as: Mathify. (2026). 标准差计算器. https://mathify.one/zh/math/standard-deviation

Use Cases

Analyze test scores

Teachers and students can use the calculator to understand the spread of exam results, identifying how consistent performance is across a class.

Example: Enter scores like 85, 90, 78, 92, 88 to see the standard deviation.

Quality control in manufacturing

Engineers can measure variability in product dimensions or weights to ensure consistency and meet quality standards.

Example: Input measurements like 10.2, 10.5, 10.1, 10.3 to check process variability.

Frequently Asked Questions

What is the difference between population and sample standard deviation?
Population standard deviation measures the spread of an entire population, using all data points. Sample standard deviation estimates the spread of a population based on a sample, using n-1 in the denominator to correct bias. Use population when you have all data, sample when you have a subset.
How do I use the standard deviation calculator?
Enter your data values separated by commas or spaces. The calculator will compute both population and sample standard deviation, along with variance. Ensure you enter numeric values only and separate them correctly.
What does variance mean in statistics?
Variance is the average of the squared differences from the mean. It measures how far each number in the set is from the mean. Standard deviation is the square root of variance, providing a measure of spread in the same units as the data.

Tips & Common Mistakes

Tips

  • Ensure your data is numeric and separated by commas or spaces for accurate calculation.
  • Use population standard deviation when your data represents the entire group; use sample for a subset.
  • Check for outliers before interpreting standard deviation, as extreme values can inflate the result.
  • Remember that standard deviation is always non-negative; a value of 0 means all data points are identical.

Common Mistakes to Avoid

  • Confusing population and sample standard deviation, leading to incorrect conclusions.
  • Entering non-numeric characters or mixing delimiters, causing errors in calculation.
  • Using standard deviation to compare datasets with different units or scales without proper normalization.

Last updated: August 13, 2026