Today we started working on collating all the work Jared has done on his long-term project on outliers into a PowerPoint presentation. We're not only concerned with incorporating the material, but also with learning how to put a scientific presentation together, paying attention to details such as citations, logical threads, layout, and consistency.

Continuing on from reviewing Jared's test from last week, we concentrated a bit more on calculating and applying the concept of margins of error. We not only reviewed the problems that Jared had some (minor) difficulties with on the test last week, but also examined fresh problems.

So as to make up for next week's classes, these classes that are replacing the Chemistry hours are a bit of a combination of Algebra and Statistics. For the Algebra part, we continued studying natural logarithms, specifically by examining a problem involving launching rockets. The fascinating part about rocket launches is the continuously changing ratio of the mass of the rocket, since as fuel is burned during the firing time the total mass of the rocket is therefore changing with altitude. As always, Jared had plenty of questions regarding the early space race that I was happy to discuss with him. We then reviewed the remaining problems on the Statistics tests from last week that Jared had for homework involving the margin of error and completing a table on not mutually exclusive probabilities, given certain information. We also watched a bit more of the lecture given by Nobel-winner Prof. Kroto, and ended up investigating topics ranging from penicillin to the early history of anesthesia. Again, Jared's scientific curiosity is very prevalent, and it would be wonderful to know that his thirst for understanding the world around him will prevail throughout his college years.

As planned, Jared sat the test on probability theory today, specifically concentrating on simple probabilities and combining them in mutually exclusive or not mutually exclusive scenarios. Jared focused well, and after he completed the assigned problems we looked through both today's test and the test he took the other day on measures of center. He did well on both tests, but encountered minor difficulties in a problem or two on each. Jared will work through those problems this weekend, and we will review his work next week.

I'd like Jared to sit a final test tomorrow on Probabilities. Hence, we spent this class reviewing the material on combining probabilities, and therefore analyzing whether situations represented independent or dependent events, and in the case of the latter whether they were mutually exclusive or not. We also reviewed conditional probabilities, and worked through a problem illustrating the usefulness of a probability tree.

Jared sat the test on measures of center in today's class. He concentrated very well for the duration of the examination. Jared was a bit unsure of how to tackle percentile problems, but was willing to re-learn how to work them, and then completed his test.

We reviewed the topics that will be on the Statistics test tomorrow. These included a quick run-through of measures of center (mean, median, mode), standard deviation, distributions, samples and populations.

We continued to go through her final review.

Theoretically, since we have reached the end of the review on this year's topics, Jared should sit the final test, but I decided to defer the test to next week, seeing as Jared had worked so hard in the Algebra class on the test. Instead, we finished watching 'Inside Einstein's Mind', the documentary we had started watching last week. Much of the material was on the beauty of the single equation describing Einstein's General Theory of Relativity G_mu_nu = ( 8 * PI * G / c^4 ) T_mu_nu, which basically states that gravity 'tells' matter how to move and matter 'tells' gravity to warp space-time. We were treated to lots of interesting algebra, and mainly, scientific concepts. Again, as in the past when watching documentaries, Jared was fully engaged.

In finalizing our review on the year's topics, today we revisited samples and random samples. In most situations, it is impractical to survey or analyze every element in a population, so therefore one selects a sample (a subset of the population). It is important that that sample is random, and therefore representative of the population as a whole, otherwise the results may end up being skewed. We then looked at binomial and normal distributions. Normal distributions, when plotted, illustrate the concept of standard deviation nicely.