For univariate data Y

Skewness Coefficient = 3 x (mean - median) / σ Where, σ=Standard deviation. Coefficient of Skewness: Skewness Coefficient also known as Pearson's Coefficient of Skewness or moment coefficient of skewness is the third standardized moment. 'Excess coefficient', Encyclopedia of Mathematics, EMS Press, 2001 1994 Kurtosis calculator; Free Online Software (Calculator) computes various types of skewness and kurtosis statistics for any dataset (includes small and large sample tests). Kurtosis on the Earliest known uses of some of the words of mathematics.

₁, Y₂, ...,Y_N, the formula for skewness is:

[ g_{1} = frac{sum_{i=1}^{N}(Y_{i} - bar{Y})^{3}/N} {s^{3}} ]

where (bar{Y}) is themean, s is thestandard deviation, and N is the number of data points. Note thatin computing the skewness, the s is computed with N in thedenominator rather than N - 1.

The above formula for skewness is referred to as the Fisher-Pearsoncoefficient of skewness. Many software programs actually compute theadjusted Fisher-Pearson coefficient of skewness

[ G_{1} = frac{sqrt{N(N-1)}}{N-2} frac{sum_{i=1}^{N}(Y_{i} - bar{Y})^{3}/N} {s^{3}} ]

This is an adjustment for sample size. The adjustment approaches1 as N gets large. For reference, the adjustment factor is1.49 for N = 5, 1.19 for N = 10, 1.08 for N = 20,1.05 for N = 30, and 1.02 for N = 100.

The skewness for a normal distribution is zero,and any symmetric data should have a skewness near zero. Negative valuesfor the skewness indicate data that are skewed left and positive values forthe skewness indicate data that are skewed right. By skewed left, wemean that the left tail is long relative to the right tail. Similarly,skewed right means that the right tail is long relative to the left tail.If the data are multi-modal, then this may affect the sign of theskewness.

Some measurements have a lower bound and are skewed right. Forexample, in reliability studies, failure times cannot be negative.

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It should be noted that there are alternative definitions of skewness inthe literature. For example, the Galton skewness (also known asBowley's skewness) is defined as

[ mbox{Galton skewness} = frac{Q_{1} + Q_{3} -2 Q_{2}}{Q_{3} - Q_{1}} ]

where Q₁ is the lower quartile, Q₃is the upper quartile, and Q

How To Calculate Skewness Coefficient

Coefficient Of Skewness

₂ is the median.

The Pearson 2 skewness coefficient is defined as

[ S_{k_2} = 3 frac{(bar{Y} - tilde{Y})}{s} ]

How To Compute Coefficient Of Skewness

Coefficient Of Kurtosis Calculator

where ( tilde{Y} ) is the sample median.

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There are many other definitions for skewness that will not bediscussed here.