Symmetric and Asymmetric DistributionsFrequency distribution can have two different shapes: Symmetric or asymmetric distribution. Asymmetric distribution can be positively skewed and negatively skewed distribution. Symmetric Distribution When the data values are evenly distributed about the mean, a distribution is said to be a symmetric distribution. A symmetry distribution ( normal distribution) resembles a bell-shape where the left portion of the distribution is equal to the right portion of the distribution. In addition, when the distribution is symmetric/unimodal , the mean, median, and mode are the same and are at the center of the distribution. Asymmetric Distribution —When there is higher density of observations on either side of the distribution, then the distribution is said to be an asymmetric distribution or Skewed (the majority of data values fall to the left or right of the mean). Skewness --Skewness is the degree of departure from symmetry of a distribution. In a positively skewed or right-skewed distribution, the majority of data values fall to the left of the mean and cluster at the lower end of the distribution. The tail of the distribution goes to the larger values . In other words, the tail is to the right. In a positively skewed distribution, the value of mean is grater than median and median is grater than mode. For example, if an instructor gave an examination and most of the students did poorly, their scores would cluster on the left side of the distribution. A few high scores would would fall on the right side of the distribution. In a negatively skewed or left-skewed distribution, the majority of the data values fall to the right of the mean and cluster at the upper end of the distribution, with the tail to the left. The tail of the distribution goes to the smaller values . In a negatively skewed distribution, the value of mean is less than median and median is less than mode. For example, If an instructor gave an examination and majority of students got very high score on an instructor’s examination. These scores would cluster on the right of the distribution. A few low scores would fall on the the tail of the distribution. Another characteristic of a frequency distribution is Kurtosis. --Kurtosis refers to the flatness or the peakedness of a distribution. —A distribution can be Leptokurtic, Mesokurtic or Platykurtic. Leptokurtic Distribution A distribution with a high peak. It is more peaked than the normal distribution. Mesokurtic Distribution A distribution with a medium peak and resembles a bell shape. It is also called a normal curve. Platykurtic Distribution A distribution with low peak. It is flatter than the normal curve.
1 Comment
Peter Westfall
12/21/2022 12:51:06
Kurtosis does not measure peakedness or flatness. The beta(.5,1) distribution is infinitely peaked but has low kurtosis. Further, the.9999U(0,1) +.0001Cauchy appears perfectly flat over 99.99% of the observable data, but has infinite kurtosis.
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