**Quote:**

.. Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average.

Student 3’s average is considered to be 100%. If we denote it by

*y*, then it is 100% of

*y*, which is the same as 1 ×

*y*.

Student 1’s average is 50%

**higher**. Therefore it is (100% + 50%) of

*y*, which is the same as (1 + 0.5) ×

*y* = 1.5

*y*.

If we were told that Student 1’s average score was 50% of the student 3’s average score, then it would be 50% of

*y*, which would be the same as 0.5

*y*.