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Below is a frequency table which has data for testing a theory that students who speak a foreign language are also strong mathematics students.

The question says to draw a graph showing conditional distribution of Math grade with the ability to speak a foreign language and give my conclusions. I computed the conditional distributions of Math grade for students who speak a foreign language and drew the below graph but it was marked incorrect.

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I don not understand why this is incorrect. Do I need to draw a side-by side graph? Something like this?

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Yes, otherwise in the first graph you have conditioned only on one level of the variable "Ability to speak ...". In your second graph both levels are shown and you can see the relationship between the grades and the ability to speak a foreign language.

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  • $\begingroup$ I've been discussing with a friend. I'm not sure whether I have computed the probabilities properly. Correct me if I'm wrong; the probability should be what percent of students speak foreign language per grade - among who got grade A (0.823 = 70/85) can speak a foreign language, and 0.176 (15/85) can not speak a foreign language? $\endgroup$ – SriniShine Jun 19 '16 at 13:26
  • $\begingroup$ Ok that's conditioning on the other variable. You had math conditioned on ability first - distribution of math grade conditioned to ability "does speak": P (A / speak) = 70/100; P (B / speak) = 20/100; P (C / speak) = 10/100 but if you need "percent of students speak foreign language per grade" then use distribution of ability conditioned to math grade A: P (speak / A) = 70/85; P (doesn't / A) = 15/85 $\endgroup$ – Camila Burne Jun 19 '16 at 14:01

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