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A histogram is a visual representation of the ... The words used to describe the patterns in a histogram are: "symmetric", "skewed left" or "right", "unimodal ...
However, a symmetric unimodal or multimodal distribution always has zero skewness. Example of an asymmetric distribution with zero skewness. This figure serves as a counterexample that zero skewness does not imply symmetric distribution necessarily. (Skewness was calculated by Pearson's moment coefficient of skewness.)
Considerations of the shape of a distribution arise in statistical data analysis, where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modelling purposes. The normal distribution, often called the "bell curve" Exponential distribution
Histogram of a sample from a normal distribution – it looks fairly symmetric and unimodal This is a sample of size 50 from a right-skewed distribution, plotted as both a histogram, and a normal probability plot.
Values greater than 5/9 may indicate a bimodal or multimodal distribution, though corresponding values can also result for heavily skewed unimodal distributions. [28] The maximum value (1.0) is reached only by a Bernoulli distribution with only two distinct values or the sum of two different Dirac delta functions (a bi-delta distribution).
When the smaller values tend to be farther away from the mean than the larger values, one has a skew distribution to the left (i.e. there is negative skewness), one may for example select the square-normal distribution (i.e. the normal distribution applied to the square of the data values), [1] the inverted (mirrored) Gumbel distribution, [1 ...
The maximum distance is minimized at = (i.e., when the symmetric quantile average is equal to =), which indeed motivates the common choice of the median as a robust estimator for the mean. Moreover, when α = 0.5 {\displaystyle \alpha =0.5} , the bound is equal to 3 / 5 {\displaystyle {\sqrt {3/5}}} , which is the maximum distance between the ...
The accompanying plot of skewness as a function of variance and mean shows that maximum variance (1/4) is coupled with zero skewness and the symmetry condition (μ = 1/2), and that maximum skewness (positive or negative infinity) occurs when the mean is located at one end or the other, so that the "mass" of the probability distribution is ...