Accumulate, count, extremum, search

The three accumulation patterns (declare outside, update inside):

// total
int sum = 0;
for (int x : arr) { sum += x; }

// count matching a rule
int evens = 0;
for (int x : arr) { if (x % 2 == 0) evens++; }

// extremum — seed with the first element, not 0
int max = arr[0];
for (int i = 1; i < arr.length; i++) {
    if (arr[i] > max) {
        max = arr[i];
    }
}

Why seed with arr[0]? Seeding max = 0 is wrong for all-negative arrays (the answer would be 0, an element that isn't even there) and max = Integer.MIN_VALUE works but obscures intent. Seeding with the first element is the exam's preferred style.

Average = sum / count — cast the sum first: double avg = (double) sum / arr.length;

Searching for a position (linear search):

public static int indexOf(int[] arr, int target) {
    for (int i = 0; i < arr.length; i++) {
        if (arr[i] == target) {
            return i;          // found: position
        }
    }
    return -1;                 // not found convention
}

-1 as "absent" is a universal Java convention — it can never be confused with a real index.