Statistics and probability
Conditional distributions and relationships
Example: College grades
A small private college was curious about what levels of students were getting straight A grades. College officials collected data on the straight A status from the most recent semester for all of their undergraduate and graduate students. The data is shown in the two-way table below:
A distribution in the data is highlighted below.
What type of distribution is this?
What conclusion can we draw from the highlighted distribution?
Officials at the college are curious if one level of student was more likely to get straight A's than the other.
Calculate the conditional distribution of straight A status for each level of student.
Based on these conditional distributions, what can we say about the association between student level and straight A status?
For this college, is there an association between the level of student and whether or not the student has straight A's?
Want to join the conversation?
- In the answer options of the problem 4, what is the difference between the option B and C? I think both answers are correct. Are not they?(36 votes)
- Choice C is like this :
C: Straight A students ( Total is 300 students ) were more likely to be graduate ( 60 students) than undergraduate ( 240 students) !
in other words; if all students who got Straight A (graduate + undergraduate) gathered in one class, then most of them would be graduate or undergraduate?(13 votes)
- Example problems are helpful and all, but how come there aren't any written definitions for what Marginal and Conditional Distribution are?(23 votes)
- Yes, they are not very straightforward. I use statology.com to help with definitions, because math has so many. Marginal distributions compare one variable to a whole population. Ex: number of females in U.S versus the whole U.S population. Conditional distributions compare a variable to a subpopulation. Ex: Proportion of women in the U.S who are married.(3 votes)
- The wording is SO confusing to me.
You wrote in Problem 3:
"Calculate the conditional distribution of straight A status for each level of student."
How do I know if I should focus on the OF (straight A) or the FOR (each level of student)? Do I calculate row or column?
Either I am stupid in English or it is really confusing.
Please someone help me?(17 votes)
- We're finding the conditional probability of x (the numerator) for each of y (clue that it should go in the denominator).
If they asked "Find the conditional probability of level of study for straight A status" then these would be reversed.(6 votes)
- Why is there an association? There is only a 6% difference between undergraduates with all A's and graduates with A's. That is almost an opinion based question(5 votes)
- I believe that Problem 2 is ambiguous, as it asks for one correct answer which is C, but both B and C appear to be correct answers. B says "There are far more students without straight A's than there are with straight A's.", which seems to be true, given a ratio of 4200 to 300.(0 votes)
- From the author:Problem 2 asks what conclusion we can draw from the highlighted distribution, and the highlighted distribution only tells us about the ratio of undergraduate to graduate students.(11 votes)
- The explanation of the first example states that "A conditional distribution turns each count in the table into a percentage of individuals who fit a specific value of one of the variables.", but in the exercise the values aren't always percentages; just counts! Is the article definition incorrect?(4 votes)
- From the author:That definition is correct! The first conditional distribution in this article appears in Problem 3.(2 votes)
I'm looking into doing AP Statistics next year, for my senior year of high school, and am wondering what prerequisites I need. Algebra 1? Algebra 2? Geometry? Precalc? Calc?
Thank you in advance!
- I did Alg 1 through Geometry before I did AP Stats, but you certainly don't need any sort of calculus class to do AP Stats.(3 votes)
- Question 5: Is a 6 procent difference enough to conclude that there is a correlation between the two variables?(3 votes)
- It depends on alpha level set by the researcher. If it is .05 it won't pass. If it is .1 it will pass.(3 votes)
- A typo? 240/360≈67%. should be 240/300 = 80%(2 votes)
- Uhh... do you see what you did there?
You said 240/360 = 67% (their answer is right), and then you said that 240/300 should be equal to 80% (that is also correct), you change the denominator from 360 to 300. lol(2 votes)
- I have a quick question about Problem 4.
It says the third choice is wrong because "Note: The third choice is wrong because there are 300
total students with straight A's, and a majority of them
240/360≈67% were undergraduate students. This doesn't mean that undergraduate students are more likely to have straight A's though. There were a lot more undergraduate students than graduate students in general, so a lot of the straight A's students are undergraduates. However, a low percentage of undergraduate students had straight A's."
I think that should be 240/300 = 80% rather than 240/360 = 67%.(2 votes)