Introduction

In statistical analysis, understanding the shape of a distribution is crucial for the correct interpretation of data. Beyond the mean and standard deviation, two additional parameters describe the distribution: skewness and kurtosis. These concepts are related to the shape, symmetry, sharpness, or flatness of the distribution and provide important information about how normally or extremely values are distributed within a dataset.

Definition of Skewness

Skewness is the measure that shows the degree of asymmetry in a distribution. A distribution is considered symmetric when its shape is similar on the left and right of the central point. When this does not occur, skewness appears. When skewness is positive, the tail of the distribution extends to the right, meaning that there are relatively few but very large values that increase the mean. When skewness is negative, the tail extends to the left, indicating the presence of extremely small values that decrease the mean. In an ideal normal distribution, skewness is approximately zero, which indicates symmetry. The skewness coefficient, also known as the coefficient of asymmetry, is used to quantify this deviation, showing the extent to which observations converge or diverge from the mean value.

Definition of Kurtosis

Kurtosis refers to the sharpness or flatness of the peak of a distribution compared to the normal distribution. It describes the degree of concentration of the data around the mean and reveals whether values are more clustered or more dispersed. When kurtosis is platykurtic, that is, less than three, the distribution has a flatter peak with more values located away from the mean. When it is mesokurtic, equal to three, the distribution has a balanced peak similar to the normal distribution. Conversely, when it is leptokurtic, greater than three, the distribution has a sharper peak with most values clustered near the mean, while at the same time showing thick tails in extreme values. Unlike skewness, which relates to symmetry, kurtosis emphasizes the likelihood of extreme values and reveals the intensity with which they influence the distribution.

Relationship between Skewness and Kurtosis

Skewness and kurtosis are not independent concepts, since both describe aspects of the distribution’s shape. Skewness focuses on symmetry, while kurtosis on the concentration of values and the likelihood of extreme observations. A distribution may be symmetric but also leptokurtic, showing a sharp peak, or it may be skewed yet have kurtosis similar to that of the normal distribution. Examining these two measures together provides a more comprehensive picture of the nature of the data and is particularly useful when evaluating whether a sample deviates from normality.

Statistical Interpretation and Uses

Understanding skewness and kurtosis is essential in statistical analysis. Through these parameters, one can assess whether the choice of parametric tests, which rely on the assumption of normality, is appropriate. At the same time, these measures highlight the presence of outliers, which can distort results and negatively affect the validity of conclusions. Their importance is equally significant in practical applications. In financial data, for example, a distribution with high leptokurtosis indicates an increased risk of extreme losses, while in biological or social studies, recognizing skewness can lead to safer data interpretation and more reliable conclusions.

Related Note

Although there are theoretical guidelines for interpreting skewness and kurtosis, these values cannot be treated with fixed rules in every case. Their significance depends on the analytical context, the type of data, and the purpose of the study. The same value of kurtosis or skewness may carry different weight in different scientific fields, making their prudent and comparative use necessary.

Conclusion

Skewness and kurtosis are fundamental statistical measures that describe the shape of distributions. Skewness refers to the degree of symmetry, while kurtosis to the sharpness and concentration of data around the mean. Studying them together provides valuable information about the reliability, normality, and structure of the data. Therefore, these two measures are not limited to theoretical statistics but find application in every scientific and research field where an accurate understanding of the data distribution is essential.