1. The problem is to find the median of a data set without explicitly counting all the values. 2. The median is the middle value when the data is ordered from smallest to largest. 3. If the number of data points $n$ is odd, the median is the value at position $\frac{n+1}{2}$. 4. If $n$ is even, the median is the average of the values at positions $\frac{n}{2}$ and $\frac{n}{2} + 1$. 5. To find the median without counting all values, use the formula for the position of the median based on $n$. 6. For example, if $n=9$ (odd), median position is $\frac{9+1}{2} = 5$, so the 5th value in the ordered list is the median. 7. If $n=10$ (even), median position is between $\frac{10}{2} = 5$ and $6$, so median is average of 5th and 6th values. 8. This rule allows you to find the median position without counting all values individually, just knowing $n$. 9. Remember, the data must be sorted to apply this rule correctly.