# Dictionary Definition

skewed adj : having an oblique or slanting
direction or position; "the picture was skew" [syn: skew]

# User Contributed Dictionary

## English

### Adjective

skewed### Verb

skewed- past of skew

# Extensive Definition

## Definition

Skewness, the third standardized
moment, is written as \gamma_1 and defined as

- \gamma_1 = \frac, \!

where \mu_3 is the third moment
about the mean and \sigma is the standard
deviation. Equivalently, skewness can be defined as the ratio
of the third cumulant
\kappa_3 and the third power of the square root of the second
cumulant \kappa_2:

- \gamma_1 = \frac. \!

This is analogous to the definition of kurtosis, which is expressed as
the fourth cumulant divided by the fourth power of the square root
of the second cumulant.

For a sample of n values the sample skewness
is

- g_1 = \frac = \frac, \!

where x_i is the ith value, \bar is the sample mean,
m_3 is the sample third central
moment, and m_2 is the sample
variance.

Given samples from a population, the equation for
the sample skewness g_1 above is a biased
estimator of the population skewness. The usual estimator of
skewness is

- G_1 = \frac

where k_3 is the unique symmetric unbiased
estimator of the third cumulant and k_2 is the symmetric unbiased
estimator of the second cumulant. Unfortunately G_1 is,
nevertheless, generally biased. Its expected value can even have
the opposite sign from the true skewness.

The skewness of a random variable X is sometimes
denoted Skew[X]. If Y is the sum of n independent
random variables, all with the same distribution as X, then it can
be shown that Skew[Y] = Skew[X] / √n.

Skewness has benefits in many areas. Many
simplistic models assume normal distribution i.e. data is symmetric
about the mean. The normal distribution has a skewness of zero. But
in reality, data points are not perfectly symmetric. So, an
understanding of the skewness of the dataset indicates whether
deviations from the mean are going to be positive or
negative.

## Pearson skewness coefficients

Karl Pearson
suggested two simpler calculations as a measure of skewness:

- (mean - mode) / standard deviation
- 3 (mean - median) / standard deviation

## External links

- An Asymmetry Coefficient for Multivariate Distributions by Michel Petitjean

skewed in Czech: Koeficient šikmosti

skewed in German: Schiefe (Statistik)

skewed in French: Asymétrie (statistique)

skewed in Spanish: Asimetría

skewed in Finnish: Vinous

skewed in Hebrew: צידוד (סטטיסטיקה)

skewed in Hungarian: Ferdeség

skewed in Italian: Simmetria (statistica)

skewed in Japanese: 歪度

skewed in Latvian: Asimetrijas koeficients

skewed in Lithuanian: Asimetrijos
koeficientas

skewed in Dutch: Scheefheid

skewed in Polish: Współczynnik skośności

skewed in Portuguese: Obliquidade

skewed in Russian: Коэффициент асимметрии

skewed in Sundanese: Skewness

skewed in Turkish: Çarpıklık

# Synonyms, Antonyms and Related Words

agee,
agee-jawed, askance,
askant, askew, askewgee, asquint, asymmetric, awry, catawampous, catawamptious, cockeyed, crooked, deflected, deflective, diffracted, diffractive, diffuse, diffused, disparate, dispersed, disproportionate,
distorted, flectional, flexed, ill-matched, ill-sorted,
inadequate, inflective, insufficient, irregular, mismatched, odd, out of proportion, refracted, refractile, refractive, refrangible, scattered, skew, skew-jawed, slaunchways, squinting, unequal, uneven, wamper-jawed, wry, yaw-ways