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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:
UndergraduateGraduateTotal
Straight A's24060300
Not3, comma, 7604404, comma, 200
Total4, comma, 0005004, comma, 500
Problem 1
A distribution in the data is highlighted below.
What type of distribution is this?
UndergraduateGraduateTotal
Straight A's24060300
Not3, comma, 7604404, comma, 200
Totalstart color #1fab54, 4, comma, 000, end color #1fab54start color #1fab54, 500, end color #1fab54start color #1fab54, 4, comma, 500, end color #1fab54
Choose 1 answer:
Choose 1 answer:

problem 2
What conclusion can we draw from the highlighted distribution?
Choose 1 answer:
Choose 1 answer:

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.
UndergraduateGraduateTotal
Straight A's24060300
Not3, comma, 7604404, comma, 200
Total4, comma, 0005004, comma, 500
UndergraduateGraduate
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?
Choose 1 answer:
Choose 1 answer:

Problem 5
For this college, is there an association between the level of student and whether or not the student has straight A's?
Choose 1 answer:
Choose 1 answer:

Want to join the conversation?

  • mr pink red style avatar for user Mahamud Hasan
    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?
    (1 vote)
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    • piceratops ultimate style avatar for user Mahmood Salah
      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?
      (1 vote)
  • leafers seed style avatar for user FotoLina3
    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?
    (13 votes)
    Default Khan Academy avatar avatar for user
    • aqualine tree style avatar for user Varsha
      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.
      (0 votes)
  • male robot hal style avatar for user Jannie Gerber
    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)
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  • blobby green style avatar for user timkoenders2
    Question 5: Is a 6 procent difference enough to conclude that there is a correlation between the two variables?
    (3 votes)
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  • blobby green style avatar for user Frank Harvey
    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)
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  • blobby green style avatar for user gameboyjustin
    Example problems are helpful and all, but how come there aren't any written definitions for what Marginal and Conditional Distribution are?
    (1 vote)
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  • aqualine tree style avatar for user Varsha
    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)
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  • blobby green style avatar for user tonykeith44
    A typo? 240/360≈67%. should be 240/300 = 80%
    (2 votes)
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  • starky sapling style avatar for user Isabella Nicolè
    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
    (1 vote)
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  • cacteye green style avatar for user 22alyson.tripp
    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
    (2 votes)
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