Here's a sample problem I just made up:

1/5 of the 20 students in a class scored 80 on a test, and the remaining students scored 100. What was the average test score for the class?

Formula (version 1)(fractional weighting)(score) + (fractional weighting)(score) = weighted average score

(1/5)(80) + (4/5)(100) = 16 + 80 = 96

Formula (version 2)[(subtotal # of students)(score) + (subtotal # of students)(score)]/[total # of students] = weighted average score

[(4)(80) + (16)(100)] /20 = [320+1600]/20 = 1920/20 = 96

{Note that the two formulas are equivalent, as fractional weighting = subtotal # of students/total # of students, e.g. 1/5 = 4/20}Portion of the differenceThe weighted average will always be betweent the two values/scores/amounts/etc. Here, it must be between 80 and 100, but where in between?

The difference is 20 = 100-80.

The 1/5 of students who score low pull the average score down from 100 by 1/5 of 20: 100-4 = 96

The 4/5 of students who score high pull the average score up from 80 by 4/5 of 20: 80 + 16 = 96

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Emily Sledge | Manhattan GMAT Instructor | St. Louis

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