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Skewness Calculator

Skewness Calculator

Data (space/comma separated)

✓Skewness

Skewness
0.7594
Mean
5.9091
SD
3.1130
Positively skewed (right tail)
🌐

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.

What is 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.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

सूत्र

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

Variable Legend

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प्रतीकनावएककवर्णन
Xdata set——
μmean——
σstandard deviation——
ssample standard deviation——

How to Skewness Calculator

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

Worked Examples

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Example 1
Given:Income data with a few very high earners
परिणाम:Positively skewed (right tail); mean > median
Example 2
Given:Test scores where most are near the top
परिणाम:Negatively skewed (left tail)

Real-World Applications

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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

⚙️

Hypothesis testing

Skewness Interpretation

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SkewnessDescriptionExample
< −1Highly left-skewedRetirement ages
−1 to −0.5Moderately left-skewedTop exam scores
−0.5 to 0.5Approximately symmetricHeights
0.5 to 1Moderately right-skewedHouse prices
> 1Highly right-skewedWealth distribution

Frequently Asked Questions

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Q

What does skewness tell us?

A

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

Q

When is data considered skewed?

A

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

Q

How is skewness different from kurtosis?

A

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

Formula-verified for precision
Reviewed October 2026
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