respond to peer discussion post regarding quartiles

This is a discussion post that you will have to respond to one of my peers. It will include the instructions for the discussion post in which peer responds. You need to respond to peers post.. No word count is necessary.

TURNITIN Score must be at or below 12%. I will be checking also myself for the score. Thank you.


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?)

Howard response below:

For this week’s discussion I decided to discuss topic one; what are some examples other than temperature where similar averages can be associated with very different distributions? As a huge baseball fan I found the topic of pitcher’s ERA’s to be rather interesting. Baseball is a game formed largely on averages and statistics. In the video the example used was the median temperature between New York and San Francisco. In New York the median temperature for the year is 55 degrees while in San Francisco it is only two degrees higher at 57 degrees. The way that each city gets to this average is quite different though. In the case of San Francisco the temperature stays pretty consistent throughout the year, while in New York the summers are really hot and the winters are really cold making the average somewhere in the middle. The same can be used when thinking about a pitcher’s ERA in baseball. The acronym ERA stands for earned run average and is used to give an average of how many runs a pitcher would give up per nine innings of pitching. Two pitchers can end up with the same ERA and go about getting there in two totally different ways. For example let’s say Pitcher A pitched 54 innings and gave up 18 runs. To figure out this pitchers ERA you take the 54 innings and divide it by the nine innings that you are trying to figure out the ERA for. Doing this you come up with 6. You then take the 18 runs Pitcher A has given up and divide it by 6 (number of complete 9 innings) to come up with an ERA of 3.00. All this is saying is that on average Pitcher A will give up 3 earned runs per every 9 innings pitched. Now let’s say Pitcher B pitched far fewer innings and got injured. Pitcher B pitched 3 innings and gave up 1 run. You would take the 3 innings and divide that by 9 giving you.333. You then take the 1 run Pitcher B has given up and divide it by the .333 giving Pitcher B an ERA of 3.00. So even though they both have the same ERA, the routes they took to get there are totally different. Batters also use averages as a measure of success in baseball. Just like with the ERA, batters can attain the same batting average even though they may get there in two totally different ways. Using the example of Batter A and Batter B who both have .300 averages; only time failing 7 out of 10 times can still be considered a success. Batter A has 3 hits out of 10 at bats; simply take the hits and divide it by the at bats. Doing this simple math you come up with .300. Now Batter B has compiled 300 hits out of 1000 at bats over a three year period. Using the same math you take the 300 hits and divide it by the 1000 at bats to get an average of .300. Little baseball history the highest single season batting average was achieved by Nap Lajoie in 1901 with a .426 batting average. In 1880 Tim Keefe recorded the lowest single season ERA in baseball history with a 0.86 ERA. END OF RESPONSE.


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