Jared appeared a bit perplexed with the material we had covered yesterday regarding Standard Deviations. I'm glad he mentioned his hesitations, since this gave me the opportunity to cover this all-important topic with him in some more depth. His interest in Statistics is unflagging, I look forward to exploring forthcoming topics with Jared.

For our first foray into the 'real' tools of statistical analysis, we explored the concept of Standard Deviation. It is most important for understanding the spread of values within a dataset. Simply quoting the mean of a dataset gives one a general handle on the numbers involved, but with the standard deviation one has a much better idea of the general parameter space one is working with within the dataset. For example, the standard deviation is very sensitive to outliers; so the difference between simply quoting the mean and quoting the mean with its standard deviation in the latter case carries a lot more information.

Jared worked through problems in which he had to calculate the measurements of center of the dataset presented (mean, median, mode, midrange). This is simply arithmetic, and as I had noted last week, Jared really knows his elementary statistics! But the underlying exercises focused on whether these measurements of center were useful in the specific contexts (e.g. for some datasets, variations in time are more important than the actual numbers). After each problem we discussed these points, and Jared was spot on every time.

Jared had worked so hard this week, so for our Statistics class today we continued with our real-life examples of how Probability works. We tested the outcomes of rolling two dice. Everybody knows that with one die the probability of getting any of the six numbers is 1/6. But when one introduces a second die into the equation, the probability does not become a straightforward 1/12. It was great fun to observe Jared as the penny dropped, and he understood how the probabilities worked.

After a walk-through of the main points from the last few lessons where we reviewed some of the terminology related to graphing and, mainly, discussed its significance, we finally delved into the start of Statistics proper. We reviewed the definitions – and importance – of the 'mean', 'median', and 'mode' of a dataset. Again, Jared expressed quite a keen interest in the topic, and remembered remarkably well the definitions of the terms!

We continued discussing topics such as errors and uncertainties in activities such as data collecting either by experiment or by polling, for example. Jared continues to express an interest in these subjects. We then proceeded to discuss how different types of data benefit from different styles of graphs for visualization.

Today we reviewed the nomenclature used in Statistics so as to build a solid verbal foundation for when we start doing actual numerical exercises. We reviewed terms such as 'Population', 'Sample', 'Randomness', 'Systematic sampling', et cetera. Even though the class may have been construed as rather slow for someone else, Jared was absolutely engaged throughout the lesson, and we discussed at length also the implications behind faulty data collection, whether intentional or not.

We continued the topic of probability with further coin tossing experiments, and Jared duly noted that the longer one tossed the coin, the closer we got to the expected 50-50 outcome, despite randomness in the order of heads and tails. In order to demonstrate the power of mathematical rules in probability, I introduced Jared to the 'Monty Hall Problem' – we tested it using three cups and a coin. After multiple runs, during which several of the school staff participated, the 2/3 vs 1/3 rule remained pretty solid (to Jared's delight!).

Before tackling the mathematics of statistics and probability, I thought it would be interesting for Jared to discuss some of the practical aspects of these subjects. So, after yesterday's foray into data and statistics, today we discussed probability in conjunction with the homework Jared had done on tossing a coin, highlighting how often the concepts of probability are misunderstood.

In our first real foray into the world of statistics, we discussed the numerous faulty ways data can be collected and presented. These pitfalls are sadly omnipresent (usually not intentionally) and often portray a distorted view (again, usually not intentionally) to the general public of the dataset in question. We discussed how important it is to collect data in non-biased random manner from a representative sample of a population. One example is the double blind method most often used in medical experiments. Jared appeared to be very interested in all aspects of data collecting, and has an excellent grasp on different graph representations.