We went through some more problems dealing with the concepts on her exam tomorrow, then she showed me a project she is working on in this class. She needed some gaps filled in.

She was able to get her test postponed until next Tuesday, so we are doing some more preparation for that.

In our second hour, we looked at the actual setup of the experiment that detected the gravitational waves, and we revisited some of the material we covered last year when Jared took Astronomy. The current detectors (LIGO, one in Virginia, one in Washington) operate on the same principle as the Michelson-Morley experiment, when those two physicists were the first to attempt to measure the speed of light. We also covered the formation of black holes of different masses - to get a black hole of some 20-30 times the mass of the Sun as are those thought to have produced this burst of gravitational waves, the precursor star would have to be some 100 times the mass of the Sun, and would produce the remnant black hole through a 'hypernova' explosion. I then obtained a PDF file of Kip S. Thorne's peer-reviewed paper for Jared to read on the mathematics behind the graphics for the movie 'Interstellar', in which the black hole, Gargantua, is, in fact, mathematically correctly reproduced. Jared was super concentrated throughout our lessons today, and I look forward to getting back to the curriculum on Tuesday.

We worked math geometry problems involving absolute value, 45-45-90 triangles, 30-60-90 triangles, proportions, cross-multiplying, the Pythagorean equation for three dimensional cubes, etc. (sub for Diana)

We are reviewing for her exam tomorrow on hypothesis testing.

We are going through a review packet for her exam Wednesday.

We covered a few of the more practical aspects of data collecting for correlation analyses, such as that one should eyeball the scatterplot initially to see if it is even worth applying a full-blown correlation test - if the data is all over the place, it's generally not worth embarking on the math. We also talked about the fact that the data must be paired data, and that it must be collected in a non-biased manner. We then studied the actual formula for the linear correlation coefficient for a sample that is denoted by the letter 'r'. We took the example of the study on foot length vs. height to explore how the formula works, by calculating x^2, y^2, and xy, and then calculating the sums of these, and plugging them into the formula.

Erin has a test next week on different forms of hypothesis testing, and has missed a lot of class on it. We went through some basics she must conduct a hypothesis test, and then went over a test review given by her teacher.

Following our usual few minutes' discussion on the importance of various aspects of statistics and critical thinking, we continued watching Hans Rosling's 'The Joy of Statistics' documentary. As always, I pause the video from time to time to ensure that Jared has digested certain crucial concepts. In today's segment, Hans discussed very interesting facts on the history of statistics. The concept of normal distributions was also presented, also in a historical context which illuminated several fascinating angles to normal distributions.

The Statistics textbook had a very interesting example to introduce the concept of correlation analysis: one of the earlier forays into forensic science - when it was still in its infancy in the late 1800's - involved the study of a possible correlation between foot length and height of an individual. I elaborated on this example to introduce Jared to 'paired datasets'. During the lesson, Jared and I explored the idea of paired datasets, scatterplots, and what constitutes - visually - a strong positive or negative correlation versus no correlation.