State whether each of the following statements is true or false:
$(1)$ The median of the observations $12, 13, 14, 15, 16$ is $14$.
$(2)$ The mode of the observations $1, 3, 5, 7, 9$ is $5$.

(A) $(1)$ True. The observations are $12, 13, 14, 15, 16$. Since the number of observations $n = 5$ (which is odd),the median is the value of the $\left(\frac{n+1}{2}\right)^{th}$ observation. Here,the $\left(\frac{5+1}{2}\right)^{th} = 3^{rd}$ observation is $14$. Thus,the statement is true.
$(2)$ False. The mode is the observation that occurs most frequently. In the set $1, 3, 5, 7, 9$,each observation occurs only once. Therefore,there is no mode for this data set. Thus,the statement is false.