Please consider the probability density function graphs for the beta distribution, given in the link.
For alpha=beta=2, the density is unimodal, which is to say, it has a single maximum.
In contrast, for alpha=beta=0.5, the density is bimodal; it has two maxima.
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Your distribution is unimodal and symmetrical.
It may be or may not be; however a normal distribution is unimodal.
No, the normal distribution is strictly unimodal.
Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.The Shape of a HistogramA histogram is unimodal if there is one hump, bimodal if there are two humps and multimodal if there are many humps. A nonsymmetric histogram is called skewed if it is not symmetric. If the upper tail is longer than the lower tail then it is positively skewed. If the upper tail is shorter than it is negatively skewed.Unimodal, Symmetric, NonskewedNonsymmetric, Skewed RightBimodal
No, but sometimes "average" means "mean" - when it doesn't mean median, geometric mean, or something else entirely.