How Symmetry, Modality and Kurtosis Can Explain the Distribution of the Data Set
Symmetry refers to the quality of being made up of precisely similar parts and that face each other or around an axis. It is a proportionate and a balanced similarity found in an object’s two halves, and usually, one half is always a mirror image of the other half. The skewness measures the symmetry of the distribution. A not symmetric (asymmetric) distribution that is one side does not reflect the other side; then it is skewed. This is how distribution measures the distribution of the data set. The skewness of a data set is indicated by the trailing frequencies or the “tail” of the distribution. If the tail is directed towards the right, then the skew is positive.
On the other hand, if the tail is directed towards the left, then the distribution is negatively skewed. For instance, a positively skewed distribution would include the following: 1, 1,2, 2, 2, 3, 3, 3, 9, 10. The outliers are found on the scale’s high end. On the other hand, the negatively skewed distribution might include 1, 2, 9, 9, 10, 10, 10, 11, 11, 11. In this case, the outliers would be at the low end of the scale (Silver, n.d.).
Modality measures the distribution’s significant peak numbers. One single major peak is unimodal and is one of the most common modality. Bi-modal refers to where two major peak distribution multi-modal distributions can exist (Silver, n.d.).The distribution of a data set is considered normal if it is symmetric and unimodal. Hence, modality and symmetry are applied to measure the distribution of data (Silver, n.d.).
Kurtosis refers to whether the data are light-tailed or heavy-tailed in reference to the normal distribution. This means that the data sets with high kurtosis tend to have heavy tails or outliers (1.3.5.11. Measures of Skewness and Kurtosis, 2019). Data sets that have low kurtosis, however, have light seats or do not have outliers. A uniform distribution would be the extreme case (1.3.5.11. Measures of Skewness and Kurtosis, 2019).
References
1.3.5.11. Measures of Skewness and Kurtosis. (, 2019). Nist.gov. https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm
Silver, G. L. (n.d.). Operational measures of central tendency. Applied Mathematics and Computation, 186(2), 1379–1384. https://doi.org/10.1016/j.amc.2006.07.130