Question

Database medians. You are working as a programmer for a college administration, and they ask you to determine the median GPA for all students. However, student GPAs are stored in two different databases, one for in-state students and one for out-of-state students. Assume there are n students of each type, so there are 2n students total. You’d like to determine the median of this set of 2n values, which we will define here to be the nth smallest value.

Answer 1

To determine the median GPA for all students, combine the GPAs from both databases and calculate the median.

Step-by-step explanation:

The median GPA for all students can be determined by combining the databases of in-state and out-of-state students. Here is how you can calculate the median:

1. Combine the GPAs from both databases into one list.
2. Sort the list in ascending order.
3. If the total number of students (2n) is odd, the median is the middle value of the ordered list.
4. If the total number of students (2n) is even, the median is the average of the two middle values.

For example, if there are 100 students (50 in each database), you would combine the GPAs from both databases into a list of 100 values. Then, after sorting the list, you could find the median as explained above.

Answer 2

The median is the sorted list's nth smallest value. The median will be at index n-1 if the list is 0-indexed.

# Combine GPAs from both databases all_gpas = in_state_gpas + out_of_state_gpas

Merge the GPAs from the in-state and out-of-state databases into a single list. This list will contain 2n GPAs. Sort the merged list of GPAs in ascending order. This can be done using any sorting algorithm, such as quicksort or mergesort.

The median is the nth smallest value in the sorted list. If the list is 0-indexed, the median will be at index n-1.