skewnessin

Skewness is a measure of the asymmetry of a probability distribution of a real-valued random variable about its mean. In a perfectly symmetrical distribution, like the normal distribution, the mean, median, and mode are all equal, and the skewness is zero. When a distribution is skewed, these measures of central tendency will differ.

Positive skewness, also known as right-skewness, occurs when the tail on the right side of the distribution is longer or fatter than the left side. In such cases, the mean is typically greater than the median, which is usually greater than the mode. This means that there are a few unusually high values that are pulling the mean upwards. Examples include income distributions, where a small number of high earners can significantly increase the average income.

Negative skewness, also known as left-skewness, occurs when the tail on the left side of the distribution is longer or fatter than the right side. Here, the mean is typically less than the median, which is usually less than the mode. This indicates the presence of a few unusually low values that are pulling the mean downwards. An example might be the distribution of test scores where most students score high, but a few perform very poorly.

Skewness is an important characteristic for understanding the shape of a dataset and can influence the choice of statistical methods. It is often quantified using a skewness coefficient.