So, I've been corresponding with one of CT's other AP Stat teachers, trying my best to answer some questions. It struck me that not only might this info be valuable to teachers, but to you too! This is some review stuff...
Remember your homework tonight is to read chapter 7. Do it.
For contingency tables, I'm not sure of a systematic method. I'd just check out the textbook and see how it goes. When I personally do them, I always check to see how a group is distributed among the whole. For instance, with the titanic, I'd see what percent of all passengers were in each class. Then, I'd look at the percentage of survivors by class and those who died by class; these number should reflect the overall proportions if everything was independent. For example, if Wilby high school is 30% black, 30% hispanic, 30% white, 5% asian, and 5% other, then I would expect the AP statistics class at Wilby to consist of those same proportions (ideally). The numbers within each group should reflect the overall proportions. Did that make any sense?
As for your other question, when describing a distribution's center and spread, we always report the mean/standard deviation for a symmetric curve, and median/iqr for a skewed curve. In a skewed curve the extreme values in the tail will either pull the mean up (skewed right) or down (skewed left). Since standard deviation is a measure of the average distance a data point is from the mean, these extremes in the tail will similarly "ruin" the standard deviation. Further, given which measures we use, to determine an outlier in a skewed curve we would use the fences (since they're based on IQR) and for symmetric curves we check if the z-score (distance from the mean in standard deviations) is greater than 3 (or less than -3).
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