Quiz 2

Name a variable for which the mean will likely be larger than the median. Explain. Don't use income or housing prices.

The key concept here, which nearly every paper that I read comprehended, was that the distribution of this variable must be right-skewed. The challenge, therefore, is to name a variable that could plausibly be right-skewed and describe this. Below are sample responses and my evaluations.

1. The cost of different priced shirts: 12, 14, 15, 16, 18. mean = 15, median = 13, because the decreasing orders of the numbers.
Evaluation: Although it is undeniably true that this particular list of numbers has the mean greater than the median, there are several key components lacking. First, is it explained that the cost of shirts will always be right-skewed? What if we collected more shirts? Is there acknowledgement that right-skewed distributions are important? Also, consider the 5 W's (and one H) of variables. Not all of them are relavent here, but it seems that the What and Who are important and are missing here. (What shirts? Whose shirts.) Finally, the explanation is not clear. Why does the decreasing order make the mean bigger than the median? Score (1-5 with 5 being best): 1

2. The number of books that a student must have for each class. Because on average a student that is generally taking 3 or 4 classes will constitute a book and a reader for each class, but for the rare students who don't need any books for their classes or if some students happen to have 5 or 6 classes, it will make the mean bigger than the median.

Evaluation: This response acknowledges that the shape of the distribution is important. But what's unclear to me is whether the student believes this shape is right-skewed or not. S/he writes that most students will have about 3-4 books, but a few will have more and a few will have less. This suggests a symmetric distribution, in which case the mean and median would be about the same. Score: 2

3. The costs of bottled wine. I believe that the mean of the prices of bottled wine in any given grocery store will be bigger than the median because at the grocery stores, there is always a wide selection of fairly cheap, affordable bottled wine. And then you have your couple of extremely expensive bottles of wine for sale as well. The selection of super expensive wine is not as big as the selection of cheap to average wine, therefore the median will be a lesser price than the mean of all the prices.

This gets all the points, and provides considerable detail in the description of the variable. Score: 5

4. The fastest speed at which people drive. A lot of people speed when they drive. Usually people drive like 5-10 mph over the speed limit. howeer, many people like to push their cars even faster, especially if your sample group is from the LA area. There will be outliers (those people who top out at 100+ speeds). The mean would probably be like 85-95. The median would probably be near 75-80.

Evaluation: This response is very good, and explains the central concept very clearly. My only complaint is that I'm not completely clear as to what we would be measuring here. What are the "Who?" and the "What?" Are we asking individuals what the fastest is they've ever driven? Are we looking at cars on the road and just looking at their speed as they pass a point on the road? Are we following cars and determining the fastest they drive during a particular trip? Score: 4 (maybe 4+).