Mark O. answered • 05/16/19
Learn Physics, Math, and Comp Sci from Professional Scientist
You are showing a bivariate distribution of handedness (left or right) versus height. The upper cell states that 4 out of 75 people considered were left-handed and short; 24 out of 75 were right-handed and short, 6 out of 75 were left-handed and medium height, etc. We can turn these values into probabilities by dividing each one by the total number of people, 75, and we come up with the following table:
Short Medium Tall Proportion
left handed 0.0533 0.080 0.0267 0.16
right handed 0.320 0.2667 0.2533 0.84
Proportion 0.3733 0.3467 0.280 1.00/1.00
If you look at the proportions along the far right column, this is the distribution of handedness regardless of height. This is called the marginal probability for handedness.
If you look at the bottom proportion row, you see the probability distribution for height regardless of handedness. This is called the marginal probability for height.
The word "marginal" comes from the fact that you are looking at the probabilities as calculated in the margins of the table, either the far right column or the bottommost row.
You can make another modification to the table. You want the marginal distribution for right-handed people. In this case, you can recalculate the probabilities for right-handed people versus height, but this time you would divide each value in the right-handed person row in your original table by just the number of right-handed people, which is 63. In so doing, your row would look like:
Short Medium Tall
right handed 0.38095 0.31746 0.30159
Again, each of these entries is obtained from the number in the original table divided by just the total number of right-handers, or 63. So, the entry for being short and right-handed is 24/63 = 0.38095. Notice that all of these probabilities add to 1.00.
