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## Statistics and probability

### Course: Statistics and probability > Unit 1

Lesson 3: Distributions in two-way tables# Conditional distributions and relationships

AP.STATS:

UNC‑1 (EU)

, UNC‑1.R (LO)

, UNC‑1.R.1 (EK)

CCSS.Math: ## 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 |

## 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)

- 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(3 votes)- 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)