Average Impact
Each of two students in a recently tested class has asked to have his paper rescored. One student's paper's score is fifty, which is far below the class's average. The other student's paper's score is seventy, which is close to the class's average. Willard believes that adding twenty to the lower score would raise the class's average more than would adding twenty to the higher score. Is Willard correct?
Source: B.G.'s file drawer (Bellingham)
Hint: Create some sample data that meets the stated conditions....then try to the two options. What happens? Can a picture help?
Solution Commentary: The Average = (50+70+X)/n where n is the number of scores and X is the sum of the other (n2) scores. Given the situation, the choice is between NewAverage1 = ([50+20]+70+X)/n or NewAverage2 = (50+[70+20]+X)/n. Now, how do the Associative and Commuative properties dictate that NewAverage1 = NewAverage2?
