Skewness Calculator

Skewness measures the asymmetry of a distribution.

How the Math Works

Skewness measures the asymmetry of a data distribution by comparing how far the data strays from the mean in different directions. The formula g₁ = (Σ(x−mean)³ ÷ n) ÷ σ³ calculates this by first finding each data point's deviation from the mean (x−mean), cubing these deviations to emphasize extreme values, then averaging them (÷ n). This average is normalized by dividing by the standard deviation cubed (σ³), making the skewness unitless and comparable across datasets. A positive result indicates right skew (longer tail on the right), negative means left skew, and zero suggests symmetry.

Practical Applications

To use this calculator, enter your dataset and it will compute the mean, then each (x−mean) deviation, cube these values, average them, and divide by the standard deviation cubed. This is valuable in statistics when analyzing data distributions - for example, in finance to check if stock returns are skewed toward extreme gains or losses, in quality control to detect if manufacturing processes produce asymmetric defects, or in research to determine if your data meets the normality assumptions required for certain statistical tests.

Day-to-Day Use

Understanding skewness helps you make better decisions in everyday situations involving data. When analyzing household expenses, a positive skewness might reveal that while most months have moderate spending, occasional large bills (like car repairs or medical emergencies) significantly impact your annual budget. In sports analytics, skewness can show whether performances cluster around average levels or frequently produce exceptional results. Even in social media engagement, knowing if interactions are symmetrically distributed or heavily skewed toward viral content helps set realistic expectations for reach and impact.

Worked example

4,8,15,16,23 → ~0.13 (slightly right-skewed).

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