Symmetric distribution, skewness & kurtosis

Symmetric distribution :

A symmetric distribution is a type of distribution where the left side of the distribution mirrors the right side. By definition, a symmetric distribution is never a skewed distribution. 

Skewness:

If one tail is longer than another, the distribution is skewed. These distributions are sometimes called asymmetric or asymmetrical distributions as they don’t show any kind of symmetry. 

A left-skewed distribution has a long left tail. Left-skewed distributions are also called negatively-skewed distributions. That’s because there is a long tail in the negative direction on the number line. The mean is also to the left of the peak.

A right-skewed distribution has a long right tail. Right-skewed distributions are also called positive-skew distributions. That’s because there is a long tail in the positive direction on the number line. The mean is also to the right of the peak.

The normal distribution is the most common distribution you’ll come across. 

Here is a link to a great article on skewness.

kurtosis:

Kurtosis measures how peaked the distribution is.

Kurtosis of a normal dist is zero.

Kurtosis can be negative. A negative kurtosis means the dist is even less peaked than a Gaussian dist.