What is the median of the data set $3, 1, 4, 1, 5, 9, 2$?

Solution

1. Arrange the data in ascending order: $1, 1, 2, 3, 4, 5, 9$.
2. The number of observations is $n=7$, which is odd.
3. The median is the value at the position $$\begin{array}{rl}\frac{n+1}{2}& =\frac{7+1}{2}\\ & =4\end{array}$$.
4. The fourth value in the sorted list is $3$.
5. Hence the answer is (B).