Using an if statement with arrays

At the comment step 4 I am trying to add the current array element to sum, compare the current array element to max_test and if it is larger, save it in the variable max_test. and compare the current element to min_test, if it is smaller save it in min_test. HOWEVER I am not getting the right outcome, i cannot figure out why i get

Highest test score: 4 Lowest test score: 1

instead of the proper outcome of 100 and 60 for those values

The code:

 import java.util.Scanner;

public class Grades5
{
  public static void main(String[] args)
  {
int[][] grades = {
                   { 87,  96, 100},
                   { 68,  75,  72},
                   { 99, 100,  95},
                   {100,  96,  70},
                   { 75,  60,  79},
                 };
int how_many_grades = grades.length * grades[0].length;

// -----------------
// Output the grades
// -----------------
System.out.print("           ");
for (int i = 0; i < grades[0].length; i++)
  System.out.print("Test " + (i + 1) + "  ");
System.out.println("Average");
for (int r = 0; r < grades.length; r++)
{
  int sum = 0;  // Sum of one student's tests

  // -------------------
  // Process one student
  // -------------------
  System.out.print("Student " + (r + 1) + "  ");
  for (int c = 0; c < grades[r].length; c++)
  {
    System.out.printf("%6d  ", grades[r]);                                                        // Step 1
      //sum += grades[c];                                                                     // Step 2
  }
  System.out.printf("%7.2f\n", (double)sum / grades[r].length);
}

// ----------------
// Output a summary
// ----------------
int max_test,  // Maximum test score
    min_test,  // Minimum test score
    sum = 0;   // Sum of all student tests

max_test = min_test = grades[0][0];    // Step 3
for (int r = 0; r < grades.length; r++)
{
  // -------------------
  // Process one student
  // -------------------
  for (int c = 0; c < grades[r].length; c++)
  {
                                     // Step 4
    if (grades[r][c] > max_test) 
      max_test = r; 
    if (grades[r][c] < min_test)
       min_test = r;
       sum += grades[r][c];
  }
}
System.out.println("Highest test score: " + max_test);
System.out.println("Lowest  test score: " + min_test);
System.out.printf("Average test score: %.1f\n",
                  (double)sum / how_many_grades);
  }
}