Skewness in statistics refers to a measure of the asymmetry of a probability distribution around its mean. It indicates whether data points in a distribution are concentrated more on one side than the mean compared to the other side. More specifically, skewness measures the lack of symmetry in a distribution. A skewness value of 0 indicates perfect symmetry, meaning the distribution is equally balanced around its mean. Positive skewness (>0) suggests that the tail of the distribution is longer on the right side, with more data points toward the lower end.
Negative asymmetry (<0) suggère que la queue de la distribution est plus longue sur le côté gauche, avec plus de points de données vers l'extrémité supérieure. Dans les statistiques, l'asymétrie est une mesure numérique qui quantifie l'asymétrie d'une distribution de probabilité.
Il fournit des informations importantes sur la forme et les caractéristiques des distributions de données, aidant les analystes à comprendre les tendances de la distribution et la façon dont les points de données sont distribués par rapport à la moyenne. Il existe trois principaux types d'asymétrie:
- Positive skew: also known as positive skew, occurs when the tail of the distribution is longer on the right side.
This indicates that there are more data points toward the lower values, with fewer higher outliers.
- Negative skew: Also known as negative skew, occurs when the tail of the distribution is longer on the left side. This suggests that there are more data points toward the higher values, with fewer lower outliers.
- Zero skewness: A skewness value of 0 indicates that the distribution is perfectly symmetrical around its mean.
The left and right tails of the distribution are equal in length and the data points are evenly distributed on both sides.
Kurtosis, on the other hand, is another statistical measure that describes the “tail” of a probability distribution. It quantifies the relative peak or flatness of a distribution compared to the normal distribution. A distribution with high kurtosis (leptokurtic) has a heavy tail and a sharp peak, indicating that it has more extreme values than a normal distribution.
A distribution with low kurtosis (platykurtic) has a light tail and is more spread out, with fewer outliers than a normal distribution.
In summary, skewness measures the skewness of a distribution around its mean, while kurtosis measures the peak or tail of the distribution relative to the normal distribution. Together, skewness and kurtosis provide comprehensive information about the shape, characteristics, and behavior of data distributions in statistical analysis and modeling
