Symmetric or not symmetric, that is the question.
Whether the data are evenly spread out around the average, producing a symmetric frequency plot, Or some data are disproportionately present on the right side or the left side of the average; thereby disturbing the symmetry.
To notice, to realize the shape, and by shape to say we understand the data and its general behavior.
To notice, to realize, perhaps to measure the shape — ah, there’s a catch; for measuring, should we first discern whether the data is right skewed or left skewed.
For who would know that a few extreme values on the right creates a positive skew, and a few extremes on the left creates a negative skew; that the average of the skewed data is not the same as the 50th percentile; that two datasets with same average and standard deviation can have different shapes.
That the measure of skew is
Thus shape does make a necessary measure to summarize the data, And thus the natural hue of data analysis includes all three summary statistics, average, variance, and skewness.
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