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### Course: AP®︎/College Statistics>Unit 1

Lesson 4: Statistics for two categorical variables

# Conditional distributions and relationships

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:
Straight A's$240$$60$$300$
Not$3,760$$440$$4,200$
Total$4,000$$500$$4,500$
Problem 1
A distribution in the data is highlighted below.
What type of distribution is this?
Straight A's$240$$60$$300$
Not$3,760$$440$$4,200$
Total$4,000$$500$$4,500$

problem 2
What conclusion can we draw from the highlighted distribution?

problem 3
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.
Straight A's$240$$60$$300$
Not$3,760$$440$$4,200$
Total$4,000$$500$$4,500$
Straight A's
$\mathrm{%}$
$\mathrm{%}$
Not
$\mathrm{%}$
$\mathrm{%}$

problem 4
Based on these conditional distributions, what can we say about the association between student level and straight A status?

Problem 5
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?
• 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?
• Example problems are helpful and all, but how come there aren't any written definitions for what Marginal and Conditional Distribution are?
• 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.
• 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.
• 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.
• 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
• Yes, the difference is only 6%, but graduates are twice as likely to have straight A's than undergraduates are, which is a rather large relative difference.
• Hello,
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?

Isabella
• 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.
• what does * in counts * mean
• Instead of percentage, it is just asking how many times it occurs
• 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.
• 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.