8/30: Mean and Standard Deviation (2.2)

Application 2.2 (p. 79)
Did Mr. Starnes stack his class
Mr. Starnes teaches AP Statistics, but he also does the class scheduling for the high school. There are two AP
Statistics classes—one taught by Mr. Starnes and one taught by Ms. McGrail. The two teachers give the same
first test to their classes and grade the test together. Mr. Starnes’s students earned an average score that was 8
points higher than the average for Ms. McGrail’s class. Ms. McGrail wonders whether Mr. Starnes might have
“adjusted” the class rosters from the computer scheduling program. In other words, she thinks he might have
“stacked” his class with better students. He denies this, of course.
To help resolve the dispute, the teachers collected data on the cumulative grade point averages and SAT Math
scores of their students. Mr. Starnes provided the GPA data from his computer. The students reported their
SAT Math scores. The table below shows the data for each student in the two classes. Note that the two data
values in each row come from a single student.
Did Mr. Starnes stack his class Give appropriate graphical and numerical evidence to support your
conclusion.

Data from Mr. Starnes' Class
GPA
SAT-­‐Math
One-­‐Var Stats-­‐
One-­‐Var Stats-­‐SAT-­‐
2.6 510 GPA
Math
2.7 520 mean 3.212 mean 622
2.9 570 Σx 48.193 Σx 9330
2.86 570 Σx² 156.695 Σx² 5855900
3.2 590 sx := s−₁x 0.364
sx :=
s−₁x
61.318
3.1 600
3.085 630 n 15 n 15
3.338 630 MinX 2.6 MinX 510
3.2 640 Q₁X 2.9 Q₁X 570
3.1 650 MedianX 3.2 MedianX 630
3.6 660 Q₃X 3.56 Q₃X 670
3.75 670 MaxX 3.8 MaxX 710
3.4 670
3.56 710
3.8 710