数学

Skewness Calculator

偏度计算器

Data (space/comma separated)

✓偏度

偏度

0.7594

均值

5.9091

3.1130

Positively skewed (right tail)

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Detailed Guide Coming Soon

We're working on a comprehensive educational guide for the Skewness Calculator in your language. The content below is shown in English.

是什么 Skewness Calculator?

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Skewness measures the asymmetry of a probability distribution. Positive skew (right tail) means a few large values pull the mean up; negative skew (left tail) means a few small values pull it down.

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公式

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f(x)Skewness = E[(X − μ)³] / σ³ = (Σ(xᵢ − x̄)³) / (n × s³)

变量说明

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符号	名称	单位	描述
X	data set	—	—
μ	mean	—	—
σ	standard deviation	—	—
s	sample standard deviation	—	—

如何 Skewness Calculator

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1Sample skewness = (n/((n−1)(n−2))) × Σ((xᵢ−x̄)/s)³
2Symmetric: skewness ≈ 0
3Right-skewed: mean > median > mode
4Left-skewed: mean < median < mode

例题解析

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示例 1

已知:Income data with a few very high earners

结果:Positively skewed (right tail); mean > median

示例 2

已知:Test scores where most are near the top

结果:Negatively skewed (left tail)

实际应用

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Data analysis and exploratory statistics

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Income and wealth distribution analysis

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Financial risk assessment

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Quality control limits

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Hypothesis testing

Skewness Interpretation

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Skewness	Description	Example
< −1	Highly left-skewed	Retirement ages
−1 to −0.5	Moderately left-skewed	Top exam scores
−0.5 to 0.5	Approximately symmetric	Heights
0.5 to 1	Moderately right-skewed	House prices
> 1	Highly right-skewed	Wealth distribution

常见问题

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What does skewness tell us?

Positive skewness: tail on right (long right tail). Negative: tail on left. Zero: symmetric.

When is data considered skewed?

Typically, |skewness| > 0.5 indicates noticeable skew. > 1 is highly skewed.

How is skewness different from kurtosis?

Skewness measures asymmetry. Kurtosis measures tail weight (how extreme the values are).

参考资料

›Skewness — Wikipedia

Mathematically verified

Reviewed October 2026

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