Skewness Calculator
Free skewness calculator. Compute Fisher-Pearson, Pearson, Bowley skewness. Interpret symmetric, rig
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Skewness โ Fisher-Pearson, Pearson's 1st/2nd, Bowley
Measure distribution asymmetry. Right-skewed, left-skewed, symmetric. Multiple methods with step-by-step breakdown.
Real-World Scenarios โ Click to Load
Data & Method
Histogram (Mean / Median / Mode)
Method Comparison
Skewness Illustration (Sk = 0.22)
Calculation Breakdown
For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- โข Skewness = 0 means symmetric distribution (e.g., normal)
- โข Skewness > 0 (positive): right-skewed โ long tail to the right, mean > median
- โข Skewness < 0 (negative): left-skewed โ long tail to the left, mean < median
- โข |Sk| < 0.5 approximately symmetric; 0.5โ1 moderately skewed; > 1 highly skewed
- โข SE โ โ(6/n) โ use for z-test of symmetry (Hโ: population skewness = 0)
Did You Know?
Methods Compared
| Method | Formula | Pros | Cons |
|---|---|---|---|
| Fisher-Pearson | Third moment / SDยณ | Standard, widely used | Sensitive to outliers |
| Pearson's First | (MeanโMode)/SD | Simple, intuitive | Mode unstable for continuous data |
| Pearson's Second | 3(MeanโMedian)/SD | Robust, uses median | Less sensitive than moment-based |
| Bowley | (Q3+Q1โ2Q2)/(Q3โQ1) | Very robust, quartile-based | Uses only 4 numbers |
Frequently Asked Questions
What does positive skewness mean?
Positive skew = right-skewed. The right tail is longer. Mean > median. Common for income, house prices.
What does negative skewness mean?
Negative skew = left-skewed. The left tail is longer. Mean < median. Common for age at retirement, sprint times.
Which skewness formula does Excel use?
Excel SKEW() uses the adjusted Fisher-Pearson formula: โ(n(nโ1))/(nโ2) ร mโ/mโ^1.5.
When is skewness significant?
Use z = gโ/SE where SE = โ(6/n). |z| > 2 suggests significant deviation from symmetry at ฮฑ โ 0.05.
Why use Bowley instead of Fisher-Pearson?
Bowley uses only quartiles โ robust to outliers. Use when data has extreme values.
Skewness by the Numbers
Official Data Sources
Disclaimer: Skewness is a sample statistic. For small samples, estimates are noisy. Use SE = โ(6/n) for hypothesis testing. Results are for educational purposes.
Related Calculators
Histogram Calculator
Create customizable histograms from raw data with multiple binning methods, density mode, normal overlay, descriptive statistics, and cumulative histogram.
StatisticsQuartile Calculator
Compute Q0(min), Q1, Q2(median), Q3, Q4(max) using multiple methods. IQR, Semi-IQR, Midhinge, Quartile Skewness.
StatisticsDescriptive Statistics Calculator
All-in-one: mean, median, mode, range, variance, SD, SEM, CV, skewness, kurtosis, quartiles, IQR, percentiles, min, max, count, sum. The comprehensive...
StatisticsFrequency Polygon Calculator
Create frequency polygons from grouped data. Plots midpoints vs frequencies. Supports overlaying multiple datasets for comparison. Raw data or frequency...
StatisticsMean Absolute Deviation Calculator
Compute MAD = ฮฃ|xแตข - xฬ|/n from data. Compare MAD about the mean vs MAD about the median. See relationship to standard deviation.
StatisticsMedian Absolute Deviation Calculator
Compute MAD = median(|xแตข โ median|). Robust spread measure. Normalized MAD, modified Z-scores, outlier detection (Iglewicz-Hoaglin).
Statistics