A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.

Question

$\begin{array}{1 1}Mean = 17.53, Variance = 4.89, Standard Deviation = 2.21 \\Mean = 18.53, Variance = 4.89, Standard Deviation = 2.14 \\Mean = 17.53, Variance = 5.89, Standard Deviation = 2.21 \\ Mean = 17.53, Variance = 5.89, Standard Deviation = 2.14 \end{array} $