Jared has had such an excellent week – he has worked so hard, and was so pleasingly engaged in class, that after a quick summarization of where he is with the long-term project, we spent the rest of class discussing various aspects of science. Jared would ask a question, and then we'd discuss the subject. One question had to do with the terminator on the Earth, separating daytime from nighttime, so I thought it might be interesting for Jared to see the video from Apollo 8, when humans first left the gravitational field of the Earth and circled the Moon – the astronauts' view of the Earth when they came round from the far side for the first time was breathtaking. (We never finished the video, Jared had so many insightful questions! We'll continue next week.)

Jared started collecting data for his long-term project. Today he picked certain baseball teams and located the birthdates of the current rosters. He also tracked down the birthdays of all US presidents to date. In conjunction with printing out this information, we discussed the various factors that can skew the results. We also talked about the very human instinct to see patterns where there are none. I can see that Jared has a healthy, skeptical approach to data analysis which is very important for constructing an unbiased picture of the world.

She has started to learn about confidence intervals, so we are going through the different scenarios for finding different confidence intervals.

We're finally getting down to the nitty-gritty and starting Jared's project. Jared started keeping a logbook by carefully recording the birthdates of people at the school that he had collected on slips of paper several weeks ago. For our memories' sake, we reviewed the math behind the Birthday Paradox, and Jared has notes to keep in his logbook. In addition, he started thinking about other demographics for which to collect birthday data, such as hockey teams, US presidents, Nobel prize winners.

We managed to settle down a bit for the Statistics class today, and after we reviewed what Jared had covered with the substitutes, we started discussing in more detail the project that Jared will be working on in the weeks to come. He will be looking at 'The Matthew Effect' as a follow-on to the Birthday Paradox. While working on the project, he will learn how to select the most effective way to visualize the data, and will apply the appropriate tools of statistics.

I read the list of concepts on the study sheet: Mean, median, mode, standard deviation, variance, normal distribution, probability, three approaches probability, probability notation, the addition rule, the multiplication rule, mutually exclusive events, permutations, combinations, and the birthday paradox. Jared explained to me the birthday paradox experiment, its outcome, and its implications. We also discussed real-world examples and usefulness of subjective probabilities and conjecture.

I introduced the next chapter, regarding probability distributions. We went through some terminology (discrete and continuous random variables, what is a probability distribution), and then we created a probability distribution in table form for the experiment of having a girl from 2 births. We represented the sample space (each outcome), and the corresponding probabilities. I then, touched base on what Expected Value is and how to calculate it.

I subbed for half of Diana's Statistics class. We went through quick examples of basic probability calculations, The Addition Rule, The Multiplication Rule, and Conditional Probability. It seems to come naturally to him. I think this was a little bit of a review of previous topics.

We went through different topics in the standard normal distribution, the normal distribution, and the central limit theorem (finding area/probability, finding z scores knowing area, applications, etc).

Ch. 4 Probability: Relative frequency, classical, and subjective approaches, complement, unlikely, unusual, definitions.