Suppose that the GPA (between 0.0 and 4.0) of 16000 undergrads aretabulated. A)

Question

Suppose that the GPA (between 0.0 and 4.0) of 16000 undergrads aretabulated.
A) If the average GPA is 3.1 and we are told that 9.2% have aperfect 4.0, what's the average GPA of the sub-4.0 students?
B) If instead we are told that the overall GPA is 3.1 but theaverage of the sub-4.0 students is 2.9, how many students (innumber) have 4.0s?

I'm not so sure if there's a statistical way to solve this problem,but I could only manage to use algebra to solve for part A. I got3.01 as the GPA for part A but I'm not sure if it's right.

Explanation / Answer

a) If there average is 3.1, it is as if every student has a 3.1(that would be one scenario), so the total grade points are3.1*16000 = 49600. However, 9.2% ( or .092*16000 = 1472students) have a 4.0, accounting for 5888 points. Therefore,the other 14528 students (16000-1472 = 14528 students) account forthe other 43712 points. Thus, the average for the otherstudents is 43712/14528 =3.01
b) I will do this a little differently: We can rewrite the average GPA as GPA = (GPA)(# Students)/(#Students) ---- (this may seem stupid but it will make sensesoon) GPA = (GPA)((# Students with a 4.0) + (# Studentswithout a 4.0))/(# Students) GPA = (GPA)((# Students with a 4.0) + ((# students) -(#Students with a 4.0)))/(# Students)
Total Average GPA = ((GPA of students less than 4.0)(#Students with a 4.0) +  (GPA of students less than 4.0)(#Students less than a 4.0))/(# students)
GPA = 3.1 = ((2.9)(16000-x)+(4.0)(x))/(16000) where x is thenumber of students with a 4.0
Solving for x you get that about 2909 students got a 4.0
Hope that helps

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.