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**A frequency distribution for two variables**

Cross Tabs A frequency distribution for two variables

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**M&Ms Color Distribution % according to their website**

Brown Yellow Red Blue Orange Green Plain 13 14 24 20 16 Peanut 12 15 23

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**We take a sample of M&M’s and find a sample distribution to compare to the website distribution**

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**My M&Ms data in counts 14 10 8 4 54 2 3 5 22 16 13 15 12 76 Brown**

Yellow Red Blue Orange Green Total Plain 14 10 8 4 54 Peanut 2 3 5 22 16 13 15 12 76

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**14 of the 76 M&M’s were plain brown M&M’s**

Yellow Red Blue Orange Green Total Plain 14 10 8 4 54 Peanut 2 3 5 22 16 13 15 12 76 14 of the 76 M&M’s were plain brown M&M’s

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Brown Yellow Red Blue Orange Green Total Plain 14 10 8 4 54 Peanut 2 3 5 22 16 13 15 12 76 54 of the 76 M&M’s were Plain

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**8 of the 76 M&M’s were blue 14 10 8 4 54 2 3 5 22 16 13 15 12 76 Brown**

Yellow Red Blue Orange Green Total Plain 14 10 8 4 54 Peanut 2 3 5 22 16 13 15 12 76 8 of the 76 M&M’s were blue

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**Probability To find the probability: N(event)/N(total)**

P(peanut green M&M) = N(Peanut Green)/N(Total M&M’s)

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**To find Joint Distribution, we find the probabilities of each cell by dividing by the total (76)**

Brown Yellow Red Blue Orange Green Total Plain 14/76 10/76 8/76 4/76 54/76 Peanut 2/76 3/76 5/76 0/76 22/76 16/76 13/76 15/76 12/76 76

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**My M&Ms data: With Marginal Distributions**

Brown Yellow Red Blue Orange Green Marg. for flavor Plain 18.4 13.2 10.5 5.3 71.1 Peanut 2.6 3.9 6.6 28.9 Marg. for color 21.0 17.1 19.8 15.8 100

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**Knowing that the M&M is green, what is the probability it was Peanut?**

Brown Yellow Red Blue Orange Green Total Plain 14 10 8 4 54 Peanut 2 3 5 22 16 13 15 12 76 We can focus on just the green column so the probability of Peanut is: N(Green Peanut)/N(Green) = 4/12

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**Conditional distribution of flavor for color**

We know the color of our M&M already, but now how is flavor distributed for this color?

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**Knowing that the M&M is Plain, what is the probability it is Yellow?**

Brown Yellow Red Blue Orange Green Total Plain 14 10 8 4 54 Peanut 2 3 5 22 16 13 15 12 76 We can focus on just the Plain row so the probability of Yellow is: N(Yellow Plain)/N(Plain) = 10/54

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**Conditional distribution of color for flavor**

We know the flavor of our M&M already, but now how is color distributed for this color?

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**Conditional distributions in general**

Conditional distribution of X for Y (we know Y for sure already, but we want to know the probability or % of having X be true as well):

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**Bar graphs for conditional distribution of color for both flavors**

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**Joint Distribution (In white boxes) Marginal (In gray boxed) Conditional (Given color or flavor)**

Brown Yellow Red Blue Orange Green Marg. for flavor Plain 18.4 13.2 10.5 5.3 71.1 Peanut 2.6 3.9 6.6 28.9 Marg. for color 21.0 17.1 19.8 15.8 100

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