Skewing, a term used in statistics and mathematics, is a measure of the asymmetry of the probability distribution of a random variable about its mean. The skewness value can be positive or negative, or even undefined. If the distribution is symmetric about the mean, skewness is zero.
Positive and Negative Skewing
When you have a dataset and the larger values are stretching out more towards the right side, we say those datasets are positively skewed. In this kind of distribution, the tail on the curve’s right-hand side is longer or fatter. The mean and median will be greater than the mode. It’s also known as right-skew distribution. A common example of positive skewness could be wealth in an economy.
Negative skewness is when the lower numbers of a data set become more spread out and the tail of the distribution elongates towards the left of the curve. The mean and median will be less than the mode. It’s also known as left-skew distribution. A typical example of negative skewness could be scores of an easy exam, where only a few students performed poorly.
Implications of Skewing
Skewness is quite useful to get an understanding of the data set distribution. If there is pronounced skewness in the data, then that indicates extreme values in the dataset which can be influential observations or outliers.
For instance, these extreme values may be errors or may well be an accurate representation of the data variance. Either way, skewness provides useful insights into the data that can inform decision-making or further analysis.
Skewness Calculation
Skewness can be calculated by using a formula. In basic sense, skewness is calculated as the difference of the third moment of the data set and the cube of data’s standard deviation, which is then divided by the fourth power of the standard deviation. It’s the formulas and calculation aspect that helps statisticians in determining the nature of distribution of the data set.
Skewness is an important concept in statistics and is studied in depth in the field of probability distributions. Understanding skewness can give a clear idea about the nature of data, allowing for targeted analysis and prediction. However, skewness values must be used with other statistical measures like kurtosis and variance to achieve a comprehensive understanding of the data.