Jared was very curious to see how our Powerball numbers were distributed, so we started examining them a bit more closely - ultimately we'd like to construct a frequency table, but today we got so far as tabulating the numbers. We then discussed a bit more on permutations and combinations.

Following up on yesterday's class, today we discussed the difference between probabilities and odds (the reason why our numbers didn't compute yesterday). Generally speaking, probabilities are expressed as (chances for a particular outcome) / (all possible outcomes), whereas odds are expressed as (chances for a particular outcome) : (chances against that outcome). Over the next couple of weeks, we will work on permutations and combinations in more depth, as a follow-up.

The Powerball jackpot increasing each week has generated a lot of excitement, both in the general media and at the school. Jared was so enthusiastic about wanting to share his knowledge on the statistics of lottery wins, so we refreshed our memory on probabilities. We started to work out the odds of winning the jackpot based on a selection of five white balls out of 69 and one red ball out of 26. We had quite a few other teachers joining in, and it was great to see Jared confidently discussing various scenarios with several teachers. We stumbled on just one little thing that Jared is going to solve for his homework.

From time to time I'd like to go back and review some of the earlier stuff we covered, and today we looked back at patterns in coin-tossing in the wider context of how difficult it is for people to process statistical concepts. We watched the TED talk of renowned statistician Pete Donnelly where he used this example to introduce further instances of people misinterpreting uncertainty. Part of his talk was dedicated to a famous case in the UK where a witness at a trial completely misunderstood simple probability, and nobody in the jury had the tools to question his statements - a woman ended up in jail for many years before it was pointed out that the mathematics at the trial were completely flawed. Pete Donnelly also touched on false positives, and this is a topic we shall cover in more depth next week.

We finished watching Hans Rosling's TED talk. It is gratifying to see how interested Jared is in all aspects: the data, the presentation of the data, the consequences of the interpretation of the data, and the intellect of Hans Rosling himself. We then took a look at Hans Rosling's webpage, and learned that we can replicate his graphs thanks to the fact that he has uploaded all of his data and has provided an interactive version of his charts. We are planning on different ways to explore data handling using this resource, amongst others.

We started class with a brief discussion on populations, samples, margins of error, and confidence intervals. In the next couple of days, we shall look at these elements more in-depth mathematically. We then continued watching Hans Rosling's TED talk on analyzing datasets. It was impressive to see how Jared immediately grasped the various depths of information that can be gleaned from the same dataset depending on the different ways those data are presented. We discussed the pitfalls involved when data are cherrypicked, intentionally or not, and how this can lead to grossly distorted interpretations.

It was so nice to see Jared again after the holidays! We spent the first part of the class catching up, mainly with Jared telling me of various statistics / probability things he had thought of over the holidays. For example, he wanted to share with me his thoughts on the odds of making it to the NFL (not large by any means) by showing me the numbers involved. We then started to watch a TED talk by Hans Rosling, generally considered one of the biggest data gurus on the planet. As usual, we only watched about two minutes in a ten-minute period because Jared always has so many thoughts and questions. A great start to the new semester.

This class was fun time for all concerned. I wish Jared a very Merry Christmas and Happy New Year. See you in 2016!

I had to give Jared several breaks during the test, hence we continued with that during the Statistics hour. I preferred to get the test done and out of the way. We will do a double hour of Statistics tomorrow instead. I very much appreciate that Jared complied with my request to finish the test.

The younger music students had a Winter Recital planned for today, for after lunch. Since this was a school-wide event, Jared and I participated, and enjoyed the show very much. After that, we continued discussing the content of Jared's project. We were very interested to read that in his book, 'Outliers', Malcolm Gladwell not only scrutinized the birth months of hockey players, but also mentions that baseball players are subjected to a similar cutoff date for team selection when younger. Football and basketball are not. This gave us ideas for more data gathering.