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. Please someone help me?

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.

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? Thank you in advance! 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.

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.

why do i have to do this, when will i need to use this.

statistics is a simplification of how the human brain works, the relations between facts are just as important as the facts themselves and understanding that will help you understand virtually anything. It's crucial to be able to see the whole picture AND the details AND the relationship between the details all at the same time to understand a concept.

Main content

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 1

Lesson 4: Statistics for two categorical variables

Conditional distributions and relationships

Google Classroom

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:

	Undergraduate	Graduate	Total
Straight A's	240	60	300
Not	3, comma, 760	440	4, comma, 200
Total	4, comma, 000	500	4, comma, 500

Problem 1

A distribution in the data is highlighted below.

What type of distribution is this?

	Undergraduate	Graduate	Total
Straight A's	240	60	300
Not	3, comma, 760	440	4, comma, 200
Total	start color #1fab54, 4, comma, 000, end color #1fab54	start color #1fab54, 500, end color #1fab54	start color #1fab54, 4, comma, 500, end color #1fab54

(Choice A)
This is the conditional distribution of straight A status for each level of student.
(Choice B)
This is the conditional distribution of student level for each straight A status.
(Choice C)
This is the marginal distribution of student level.
(Choice D)
This is the marginal distribution of straight A status.

problem 2

What conclusion can we draw from the highlighted distribution?

(Choice A)
There are far more students with straight A's than there are without straight A's.
(Choice B)
There are far more students without straight A's than there are with straight A's.
(Choice C)
There are far more undergraduate students than graduate students.
(Choice D)
There are far more graduate students than undergraduate students.

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.

	Undergraduate	Graduate	Total
Straight A's	240	60	300
Not	3, comma, 760	440	4, comma, 200
Total	4, comma, 000	500	4, comma, 500

	Undergraduate	Graduate
Straight A's	Your answer should be an integer, like 6 a simplified proper fraction, like 3, slash, 5 a simplified improper fraction, like 7, slash, 4 a mixed number, like 1, space, 3, slash, 4 an exact decimal, like 0, point, 75 a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text percent	Your answer should be an integer, like 6 a simplified proper fraction, like 3, slash, 5 a simplified improper fraction, like 7, slash, 4 a mixed number, like 1, space, 3, slash, 4 an exact decimal, like 0, point, 75 a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text percent
Not	Your answer should be an integer, like 6 a simplified proper fraction, like 3, slash, 5 a simplified improper fraction, like 7, slash, 4 a mixed number, like 1, space, 3, slash, 4 an exact decimal, like 0, point, 75 a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text percent	Your answer should be an integer, like 6 a simplified proper fraction, like 3, slash, 5 a simplified improper fraction, like 7, slash, 4 a mixed number, like 1, space, 3, slash, 4 an exact decimal, like 0, point, 75 a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text percent

problem 4

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

(Choice A)
Undergraduate students were more likely to have straight A's than graduate students.
(Choice B)
Graduate students were more likely to have straight A's than undergraduate students.
(Choice C)
Straight A students were more likely to be graduate students than undergraduate students.

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?

Sort by:

Mahamud Hasan
Posted 6 years ago. Direct link to Mahamud Hasan's post “In the answer options of ...”
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?
Button navigates to signup pageComment on Mahamud Hasan's post “In the answer options of ...”
(35 votes)
Answer
- Mahmood Salah
  Posted 6 years ago. Direct link to Mahmood Salah's post “Choice C is like this : ...”
  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?
  Button navigates to signup page
  (12 votes)
gameboyjustin
Posted 6 years ago. Direct link to gameboyjustin's post “Example problems are help...”
Example problems are helpful and all, but how come there aren't any written definitions for what Marginal and Conditional Distribution are?
Button navigates to signup pageComment on gameboyjustin's post “Example problems are help...”
(22 votes)
Answer
- Alexa
  Posted 5 months ago. Direct link to Alexa's post “Yes, they are not very st...”
  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.
  Button navigates to signup page
  (2 votes)
FotoLina3
Posted 4 years ago. Direct link to FotoLina3's post “The wording is SO confusi...”
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?
Button navigates to signup pageComment on FotoLina3's post “The wording is SO confusi...”
(16 votes)
Answer
- Varsha
  Posted 4 years ago. Direct link to Varsha's post “We're finding the conditi...”
  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.
  Comment on Varsha's post “We're finding the conditi...”
  (5 votes)
Troy Chaney
Posted 5 months ago. Direct link to Troy Chaney's post “he tryin to gas it up💀”
he tryin to gas it up💀
Button navigates to signup pageComment on Troy Chaney's post “he tryin to gas it up💀”
(6 votes)
Answer
Isabella Nicolè
Posted 4 years ago. Direct link to Isabella Nicolè's post “Hello, I'm looking into d...”
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?

Thank you in advance!
Isabella
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- book
  Posted 4 years ago. Direct link to book's post “I did Alg 1 through Geome...”
  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.
  Comment on book's post “I did Alg 1 through Geome...”
  (3 votes)
22alyson.tripp
Posted a year ago. Direct link to 22alyson.tripp's post “Why is there an associati...”
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
Button navigates to signup pageComment on 22alyson.tripp's post “Why is there an associati...”
(5 votes)
Answer
- allegrafaye
  Posted 2 months ago. Direct link to allegrafaye's post “Yes, the difference is on...”
  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.
  Button navigates to signup page
  (1 vote)
James Corcra
Posted 5 months ago. Direct link to James Corcra's post “what does * in counts * m...”
what does * in counts * mean
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Alex Ferreira
  Posted 5 months ago. Direct link to Alex Ferreira's post “Instead of percentage, it...”
  Instead of percentage, it is just asking how many times it occurs
  Button navigates to signup page
  (6 votes)
Frank Harvey
Posted 5 years ago. Direct link to Frank Harvey's post “I believe that Problem 2 ...”
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.
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- Jeff Dodds
  Posted 5 years ago. Direct link to Jeff Dodds's post “Problem 2 asks what concl...”
  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.
  Comment on Jeff Dodds's post “Problem 2 asks what concl...”
  (10 votes)
Jannie Gerber
Posted 6 years ago. Direct link to Jannie Gerber's post “The explanation of the fi...”
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?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Jeff Dodds
  Posted 5 years ago. Direct link to Jeff Dodds's post “That definition is correc...”
  From the author:That definition is correct! The first conditional distribution in this article appears in Problem 3.
  Comment on Jeff Dodds's post “That definition is correc...”
  (1 vote)
👑Michael Landsiedel👑
Posted 4 months ago. Direct link to 👑Michael Landsiedel👑's post “why do i have to do this,...”
why do i have to do this, when will i need to use this.
Button navigates to signup pageComment on 👑Michael Landsiedel👑's post “why do i have to do this,...”
(0 votes)
Answer
- terminata
  Posted 4 months ago. Direct link to terminata's post “statistics is a simplific...”
  statistics is a simplification of how the human brain works, the relations between facts are just as important as the facts themselves and understanding that will help you understand virtually anything. It's crucial to be able to see the whole picture AND the details AND the relationship between the details all at the same time to understand a concept.
  Button navigates to signup page
  (13 votes)