1. The problem is to find the median and mode of a given data set. 2. The median is the middle value when the data is arranged in ascending order. If the number of data points is odd, the median is the middle number. If even, it is the average of the two middle numbers. 3. The mode is the value that appears most frequently in the data set. 4. Example data set: $\{3, 5, 7, 7, 8, 10, 12\}$. 5. Arrange the data in order (already sorted here). 6. Median: Since there are 7 numbers (odd), median is the 4th number: $7$. 7. Mode: The number $7$ appears twice, more than any other number, so mode is $7$. 8. Another example data set: $\{2, 4, 4, 6, 8, 10\}$. 9. Median: There are 6 numbers (even), so median is average of 3rd and 4th numbers: $$\frac{4 + 6}{2} = \frac{10}{2} = 5$$. 10. Mode: Number $4$ appears twice, more than others, so mode is $4$. This shows how to find median and mode for data sets with odd and even counts.