Measures of location
The mean or expectation of the random variable $$X$$ is $$E[X]$$ the long-run average of realisations of $$X$$.
The mode is where the pmf or pdf achieves a maximum (if it does so).
For a random variable, $$X$$, the median is such that $$P(X\leq~ \mbox{median}) = \frac{1}{2}$$, so that 50% of values of $$X$$ occur above and 50% below the median.Percentiles $$x_p$$ is the $$(100-p)$$-th percentile of a random variable $$X$$, if $$P\left(X\leq x_p\right) = p$$. For example, the $$5$$th percentile, $$x_{0.05}$$, has 5% of the values smaller than or equal to it.
The median is the $$50$$th percentile, the lower quartile is the $$25$$th percentile, the upper quartile is the $$75$$th percentile.