Find the median and the mode for the following set of numbers.
$$2,2,3,5,5,5,6,8,9$$

The data is already arranged in ascending order: $2,2,3,5,5,5,6,8,9$.Total number of observations ($n$) = $9$ (which is odd).Median:
$$\text{Median}={\left(\frac{n+1}{2}\right)}^{\text{th}}\text{ value}={\left(\frac{9+1}{2}\right)}^{\text{th}}=5^{\text{th}}\text{ value}$$
Looking at the sequence, the 5th value is $5$.Mode:The mode is the value that occurs most frequently.$2$ occurs 2 times$3,6,8,9$ occur 1 time each$5$ occurs 3 timesTherefore, $\text{Mode}=5$.