Skewness is a measure of the asymmetry of a distribution. It is a statistical measure that describes how the values of a variable are distributed around the mean, or expected value, of the variable. A distribution is said to be skewed if the values of the variable are not evenly distributed around the mean. Skewness can be either positive or negative, depending on the direction of the asymmetry.

Positive Skewness:

Positive skewness occurs when the distribution of a variable is skewed to the right, meaning that there is a longer tail on the right side of the distribution. This is often referred to as a “right-skewed” distribution. An example of a variable with positive skewness is income. In many countries, the distribution of income is skewed to the right, meaning that there are a few individuals with very high incomes, but most individuals have lower incomes. This results in a longer tail on the right side of the distribution, indicating positive skewness.

Negative Skewness:

On the other hand, negative skewness occurs when the distribution of a variable is skewed to the left, meaning that there is a longer tail on the left side of the distribution. This is often referred to as a “left-skewed” distribution. An example of a variable with negative skewness is lifespan. In many countries, the distribution of lifespan is skewed to the left, meaning that there are a few individuals who live to very old ages, but most individuals have shorter lifespans. This results in a longer tail on the left side of the distribution, indicating negative skewness.

Skewness can be calculated using a statistical formula that takes into account the mean, median, and standard deviation of the distribution. A distribution is considered to be symmetrical if the skewness value is close to zero, indicating that the values of the variable are evenly distributed around the mean. If the skewness value is greater than zero, the distribution is positively skewed, and if the skewness value is less than zero, the distribution is negatively skewed.

Skewness is important to consider when analyzing the distribution of a variable because it can affect the results of statistical tests and analyses. For example, if a distribution is positively skewed, the mean of the distribution may be higher than the median, meaning that the average value may not accurately represent the majority of the values in the distribution. In this case, it may be more appropriate to use the median as a measure of central tendency instead of the mean.

In conclusion, skewness is a measure of the asymmetry of a distribution and can be either positive or negative depending on the direction of the skew. Positive skewness occurs when the distribution is skewed to the right, and negative skewness occurs when the distribution is skewed to the left. Skewness is important to consider when analyzing the distribution of a variable because it can affect the results of statistical tests and analyses.