For many years, the New York subway had no air conditioning on the grounds that the average trip was only 15 minutes, and 15 minutes without air conditioning is no hardship, even in the New York summer. Critique this reasoning.

Description

You will find Video 4: Variation 1: Introduction and Quartiles by navigating to the MSL Tools for Success link under Course Home. The video begins at the park, with cyclists and joggers going by. We show a very slow old woman going by on a bike, and then a bunch of racing cyclists. We point out that sometimes, what is interesting about a data set is not its average but how much it varies. We then discuss the weather in New York and San Francisco, which have pretty much the same average annual temperature, even though New York has hot summers and cold winters. Quartiles as a measure of variation are introduced by way of the price of food on take-out menus. The video ends with a practical application in medical research, where mean exposure to a toxin is far less interesting than the fact that a small number of individuals are exposed to very high levels.

Respond to one of the following questions in your initial post:

What are some examples, other than temperature, where similar averages can be associated with very different distributions? A few thoughts: costs (e.g., cost of illegally downloading a song online is the same average cost of driving above the speed limit, assuming that you are only caught speeding occasionally); ERA of pitchers (i.e., some are very consistent, others are sometimes brilliant, sometimes horrible); success rates in surgery (i.e., do we want an operation that most surgeons can do pretty well, or one in which a few surgeons are nearly perfect and some have very poor results?)

Give some practical uses of knowing variation. A few thoughts: You are traveling to a job interview; what clothes do you need to pack for a trip? Doctors need to know distributions of blood values to know whether a patient is out of range; industrial engineers need to know distributions, for example the strength of a certain part to see if there is a problem with a manufacturing machine; clothing manufacturers need to know the distribution of sizes, for example children’s clothes for a certain age.

For many years, the New York subway had no air conditioning on the grounds that the average trip was only 15 minutes, and 15 minutes without air conditioning is no hardship, even in the New York summer. Critique this reasoning.

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