Question

1. if miguel earned the following test scores 89, 92, 86, and 97, his average (mean) test score would be 91. the teacher entered his scores in as 89, 92, 68 and 97.

a) how is his mean going to change?
b) if he were to not turn in a take home test and got a 0, how would his average change?

Explanation:

Step1: Calculate original sum

The original scores are 89, 92, 86, 97. The sum $S_1=89 + 92+86 + 97=364$, and the original mean $\bar{x}_1=\frac{364}{4}=91$.

Step2: Calculate sum with wrong - entry

The scores with wrong - entry are 89, 92, 68, 97. The sum $S_2=89 + 92+68 + 97=346$, and the new mean $\bar{x}_2=\frac{346}{4}=86.5$. The change in mean is $86.5 - 91=-4.5$.

Step3: Calculate sum with 0 score

If a 0 is added, the scores are 89, 92, 86, 97, 0. The sum $S_3=89 + 92+86 + 97+0 = 364$, and the new mean $\bar{x}_3=\frac{364}{5}=72.8$. The change in mean is $72.8 - 91=-18.2$.

Answer:

a) The mean will decrease by 4.5.
b) The mean will decrease by 18.2.