Mr. Mitzel's Extra Credit Opportunity- Week 2

Welcome back O'Neill Middle School students! Last week, Mrs. Mitzel offered you some extra credit points for answering a couple math questions related to the NCAA Tournament. With the field now narrowed down to the Sweet 16, we've decided to offer another opportunity for some extra credit.

Before we get to this week's questions, here's an answer key from last week. I heard there were some questions about the answers this week, so hopefully this will clear it up a little bit.

1. You guys have learned about percents and the percent proportion, so we'll apply it to last year's NCAA Tournament bracket. Of all the "Second Round/Round of 64" games last year, what percentage of those games were "upsets"? (For those of you who aren't familiar with the NCAA Tournament or sports in general: the bracket is split up into four groups of 16 teams who receive a "seed", a number from 1 to 16. The 1 seed is the best team, the 2 seed is second best, and so on. An "upset" is where the team with a higher number seed wins over the team with the lower number seed. For example, the 12 seed beating the 5 seed would be an upset.)

Looking at the 2014 bracket, there are 32 games in the "Second Round/Round of 64". Of those games, eight met the definition of an "upset": #9 Pitt beating #8 Colorado, #12 Stephen F. Austin beating #5 VCU, #11 Dayton beating #6 Ohio State, #10 Stanford beating #7 New Mexico, #12 Harvard beating #5 Cincinnati, #12 North Dakota State beating #5 Oklahoma, #11 Tennessee beating #6 Massachusetts, and #14 Mercer beating #3 Duke. So, using the percent proportion, we multiply 8 by 100 and divide that by 32. 8*100 = 800; 800/32 = 25. So, 25 percent of the "Second Round/Round of 64" games last year were upsets. However, in talking to Mrs. Mitzel, it sounds like some of you misunderstood what I meant by "Second Round", and looked at the "Third Round/Round of 32" instead (not your fault; the NCAA is dumb). Those of you who found five upsets were correct, and out of 16 games, the correct answer would be 31.25 percent.

2. We're going to try a probability question. Starting on Thursday, the field of 64 will start playing, and by Sunday, only 16 teams (known as the "Sweet 16") will still be in the Tournament. If you pick one team out of the 64, what is the probability that they will make the Sweet 16? Express this answer as a percent (rounded to the nearest whole number), a decimal (rounded to the nearest hundredth), and a fraction.

Dictionary.com defines probability as "the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences." Basically, you're dividing the number of outcomes you want by the total number of possible outcomes. A good comparison would be to take a bag of 64 marbles. 16 are blue, 20 are red, 24 are green, and 4 are yellow, and you want to know what the probability of drawing a blue marble would be. This would mean you divide 16 by 64. 16/64 = 1/4 = 0.25 =25%.

If you have any further questions, you can leave them in the comments below or ask Mrs. Mitzel. In the meantime, here is this week's question.

1. You guys may have learned about this last year, but if not, you will have to look up how to do it (yes, you can use Google). Look at the bracket and take note of the seeds (this will be the number next to each team listed on games scheduled for either March 26th or March 27th) of the 16 remaining teams. Find the mean, median, and mode of this set of data. Round all answers to the nearest hundredth.

Like last week, please send your answers back to Mrs. Mitzel in an email by the end of school on Thursday. Mrs. Mitzel will give you an extra credit point for each of these correct answers. On top of those, for a possible additional extra credit point, look at the Sweet 16, and pick one team that you think will make the Final Four. Here's the catch: you cannot pick the same team that you picked last week. So those of you who wasted your extra credit point on Kentucky last week... sorry, I'm not sorry. If whatever team you pick does make it, you will get that bonus point.