STATISTICSDescriptive StatisticsStatistics Calculator
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Skewness Calculator

Free skewness calculator. Compute Fisher-Pearson, Pearson, Bowley skewness. Interpret symmetric, rig

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

Sk
STATISTICSDescriptive Statistics

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

skewness_results.sh
CALCULATED
$ skewness --method="fisher-pearson" --n=23
Skewness (fisher-pearson)
0.2182
Interpretation
Approximately symmetric (right/positive tail)
Mean
79.3043
Median
79.0000
Fisher-Pearson
0.2182
Pearson 1st
0.9618
Pearson 2nd
0.1202
Bowley
0.0000
Share:
Skewness
Sk = 0.2182
0.218
Approximately symmetric (right/positive tail)z = 0.43
numbervibe.com/calculators/statistics/skewness-calculator

Histogram (Mean / Median / Mode)

Mean: 79.30Median: 79.00Mode: 72.00

Method Comparison

Skewness Illustration (Sk = 0.22)

Calculation Breakdown

COMPUTATION
Mean
79.3043
\text{Sigma} x/n
COMPUTATION
Median
79.0000
50th ext{percentile}
COMPUTATION
SD
7.5945
โˆš(\text{Sigma} (x-xฬ„)^{2}/(n-1))
SKEWNESS
Fisher-Pearson gโ‚
0.2182
[n/((n-1)(n-2))] imes \text{Sigma} ((xแตข-xฬ„)/s)^{3}
SKEWNESS
Pearson's First
0.9618
( ext{Mean} - ext{Mode})/ ext{SD}
SKEWNESS
Pearson's Second
0.1202
3( ext{Mean} - ext{Median})/ ext{SD}
SKEWNESS
Bowley
0.0000
rac{Q3+Q1-2Q2}{Q3-Q1}
SIGNIFICANCE
SE(skew)
0.5108
โˆš(6/n)
SIGNIFICANCE
z (symmetry test)
0.43
g_{1}/ ext{SE}
RESULT
Interpretation
Approximately symmetric (right/positive tail)

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • โ€ข Skewness = 0 means symmetric distribution (e.g., normal)
  • โ€ข Skewness > 0 (positive): right-skewed โ€” long tail to the right, mean > median
  • โ€ข Skewness < 0 (negative): left-skewed โ€” long tail to the left, mean < median
  • โ€ข |Sk| < 0.5 approximately symmetric; 0.5โ€“1 moderately skewed; > 1 highly skewed
  • โ€ข SE โ‰ˆ โˆš(6/n) โ€” use for z-test of symmetry (Hโ‚€: population skewness = 0)

Did You Know?

๐Ÿ“ŠIncome and wealth distributions are typically right-skewed โ€” a few very high values pull the mean above the median.Source: Economics
๐ŸƒSprint times are often left-skewed โ€” most runners cluster near the fast times, with a tail of slower runners.Source: Sports
๐Ÿ“Karl Pearson developed the first and second skewness coefficients in the late 1800s. Fisher-Pearson came later.Source: History
๐Ÿ”ฌFailure times (e.g., equipment lifespan) often follow exponential or Weibull distributions โ€” highly right-skewed.Source: Reliability
๐Ÿ“ˆStock returns can have fat tails and slight skewness. Negative skew is common โ€” large drops occur more often than large gains.Source: Finance
๐ŸŒก๏ธTemperature data is often nearly symmetric. Heights and many biological measures are close to normal.Source: Natural sciences

Methods Compared

MethodFormulaProsCons
Fisher-PearsonThird moment / SDยณStandard, widely usedSensitive to outliers
Pearson's First(Meanโˆ’Mode)/SDSimple, intuitiveMode unstable for continuous data
Pearson's Second3(Meanโˆ’Median)/SDRobust, uses medianLess sensitive than moment-based
Bowley(Q3+Q1โˆ’2Q2)/(Q3โˆ’Q1)Very robust, quartile-basedUses 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: โˆš(n(nโˆ’1))/(nโˆ’2) ร— mโ‚ƒ/mโ‚‚^1.5.

When is skewness significant?

Use z = gโ‚/SE where SE = โˆš(6/n). |z| > 2 suggests significant deviation from symmetry at ฮฑ โ‰ˆ 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

0
Symmetric
0.5
Moderate threshold
1
Highly skewed
โˆš(6/n)
SE of skewness

Disclaimer: Skewness is a sample statistic. For small samples, estimates are noisy. Use SE = โˆš(6/n) for hypothesis testing. Results are for educational purposes.

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