Skewness Calculator

Skewness measures the lack of symmetry in a data set. A distribution is asymmetrical when its left and right sides do not mirror each other. The calculation relies on the third standardized moment. Specifically, sample skewness is typically computed using the adjusted Fisher-Pearson standardized moment coefficient: g1 = [n / ((n - 1)(n - 2))] * sum((xi - mean)^3) / s^3, where n is the number of values, xi represents each individual data point, mean is the arithmetic average, and s is the standard deviation. A value of zero indicates a perfectly symmetrical distribution, while positive and negative values reveal the direction of the tail.

Imagine you are analyzing test scores for a small cohort of students, and your dataset consists of five values: 60, 65, 70, 75, and 95. First, compute the mean of these values, which is (60 + 65 + 70 + 75 + 95) / 5 = 73. Next, find the standard deviation, which evaluates to approximately 13.51. For each data point, subtract the mean, cube the result, and sum them up: ((60-73)^3 + (65-73)^3 + (70-73)^3 + (75-73)^3 + (95-73)^3), yielding approximately 11,392. Finally, adjust this sum using the sample size formula to get the final skewness coefficient of roughly 1.15, indicating a right-skewed distribution where most scores are on the lower end with a high-scoring tail.

When analyzing skewness, always check your dataset for extreme outliers, as a single unusually high or low value can heavily distort the skewness coefficient and mislead your analysis. Furthermore, remember that a skewness value between -0.5 and 0.5 generally indicates that the data is fairly symmetrical, whereas values beyond +1 or -1 suggest a highly skewed distribution requiring non-parametric statistical methods or data transformation.