This is definitely possible mathematically. We are not talking about 3.3 median for all the classes but a 3.3 median for the GPA of all the students in those classes. Medians are not means and the sets (classes) are not what we are concerned about. We care about the GPA of students in those classes.Anonymous User wrote:Math-wise this is not possible. If X sets of data each has a 3.3 median, then the weighted average of all or some of these sets of data will definitely have a 3.3 median.FlowBro wrote:Curious to know this as well. How does 3.2ish put you so far down in the class? Seems closer to median to me like third quartile as a poster above said.intlsplitr wrote:Can someone explain, mathematically, how the overall median can be higher than 3.3 if every class has a strict 3.3 median?
Example:
Student A, B, and C all take two classes together in which A, B, and C are the only students.
Class 1
A receives a 3.0
B receives a 3.3
C receives a 4.0
Class median 3.3
Class 2
A receives a 3.0
B receives a 4.0
C receives a 3.3
Cass median 3.3
In both classes the median is a 3.3 and both classes have the exact same distribution of grades and therefore the same mean of 3.43. In both classes student A receives a below median grade while students B and C receive at/above median grades, that student B and C switch on.
GPAs of students after 2 classes
A-3.0
B-3.65
C-3.65
This example shows how the sets of data (the classes) need not have the same means or medians of the individual sub-components of the data (the students' GPAs). Although, this is an obviously extreme example involving just 3 students with a wide spread between an above median grade, a 4.0, and a median grade, a 3.3, it nevertheless shows the principal that I am trying to illustrate.
Further it makes sense to assume that the median GPAs of students will be higher than the median grade given in courses because of the distribution of abilities and interests. If a student lacks the underlying ability to explain and recall cases it will not matter if the case if a tort or a civil liberties case. However, if a student has a particular interest in the subject and retains the ability that median student may jump up from their typical median performance for an above median grade (or vice versa).
Also I'm not trying to call out and publicly shame anyone's suspect math abilities but that is a completely unnecessary use of anon that defeats its entire purpose.