Final Answer:
The median age of teachers in the mathematics department is 49.
Step-by-step explanation:
In order to find the median, we first need to arrange the ages in ascending order: 25, 25, 25, 37, 43, 49, 49, 53, 53, 56. Now, since there are 10 data points, the median will be the average of the 5th and 6th values. In this case, the 5th and 6th values are both 49, so the median age is 49.
Now, let's briefly explain the concept of median and its calculation. The median is the middle value of a dataset when it is ordered. In case of an even number of data points, the median is the average of the two middle values. Here, with 10 ages, the median is the average of the 5th and 6th ages when arranged in ascending order.
It's worth noting that the median is a measure of central tendency that is not affected by extreme values (outliers), making it a robust measure for describing the central position of a dataset. In this case, the median age provides a representative value for the middle of the distribution, giving us insight into the typical age of teachers in the mathematics department.