Skewness
Skewness is asymmetrical in a statistical distribution, where the curve appears distorted or concentrated either to the left or to the right. Skewness can be used to define the extent to which a distribution differs from normal distribution. When a curve or distribution in a graph is classical or symmetrical, the graph appears in a "bell-shaped curve", it will be a normal distribution curve. In this case, the mean or the average, and the mode, or maximum point on the curve is equal and the end of the lines of the graph appears as mirror images of each other. Negatively skewed distribution is also called left-skewed distribution and this is where the distribution leans on the left where there is a long left tail on the left side of the number line. The mean is always to the left of the median which explains the mean being less than the median and the mode. A right skewed has a long right tail and they are also called positive skewed distributions. The long tail on the opposite direction of the number line explains the positive skewness. The mean is to the right of the peak and to the right of the median (Ho and Yu 2015).
Skewness in Probability Theory and Statistics
Skewness is used in probability theory and statistics to measure of the asymmetry of the probability distribution of real-valued random variable about its mean. The skewness result can be positive or negative and its qualitative interpretation can be complicated and counterintuitive. According to the formula of Pearson's first co-efficient of skewness uses the mode and therefore to use it, you must know the mean, mode and/or median and standard deviation of data. Moreover, if the mode used to measure skewness is made up of two pieces of data, it won't be a stable measure of central tendency. Multimodal and discrete distribution does not enhance measuring skewness due to hard interpretation and in cases where the relationship of mean and median are to be determined, data must be transformed (Silverman 2018).
References
Silverman, B. W. (2018). Density estimation for statistics and data analysis. Routledge.
Ho, A. D., " Yu, C. C. (2015). Descriptive statistics for modern test score distributions: Skewness, kurtosis, discreteness, and ceiling effects. Educational and Psychological Measurement, 75(3), 365-388.
