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.

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标准差计算器.

计算总体标准差和样本标准差及方差

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输入数值

输入时结果会更新。

02 / 答案

输入数字(输入用逗号、空格或换行分隔的数字)

总体 (σ)

总体标准差 (σ)：当你拥有整个总体的数据时使用。除以 N。

样本 (s)

样本标准差 (s)：当你拥有的是更大总体的样本数据时使用。除以 N-1（贝塞尔校正）。

样本结果

平均数 (μ)18.0000

方差 (s²)27.4286

标准差 (s)5.2372

结果

数据个数 (n)8

总和 (Σx)144.00

Median18.5000

Mode23

极差13.00

最小值 / 最大值10 / 23

排序后的数据

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

理解标准差

解释：标准差较低意味着数据点接近平均值。标准差较高意味着数据分布在更大的范围内。

总体 vs. 样本: 总体标准差 (σ)：当你拥有整个总体的数据时使用。除以 N。样本标准差 (s)：当你拥有的是更大总体的样本数据时使用。除以 N-1（贝塞尔校正）。

Cite this calculator

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

Cite as: Mathify. (n.d.). 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