We went through her test review on correlation and regression.

Jared was sick today.

We started working on her exam review for Correlation.

Since we're covering Pascal's Triangle and combinations in Algebra, I thought this would be a good spot to start reviewing the primary concepts in our Statistics class. We started today with reviewing Permutations (and looked into Combinations in a bit more depth). We will be working our way through the topics in the weeks to come, so that at some point, Jared will be familiar with all the topics that may appear in first-year college test on Statistics. We have already covered most of them in the Fall (probability theory, measures of center, etc.) but I want to make sure that Jared is fully familiar with them, and understands the theory behind them to some extent.

I could definitely see that Jared was not feeling very well, so considering that he started our session by excitedly asking me about whether I'd heard that Scott Kelly had already returned to normal height after his 11 months in space, I decided to indulge his insatiable curiosity regarding the world around him and talk space stuff. We talked about various - historical and practical - aspects of manned space flight, getting useful instruments into orbit (without satellites, for example, there would be no GPS let alone all the other scientific detectors up there), and the implications of exploring our immediate neighborhood in the Universe. Jared also kindly remembered that I was going to go observing at the weekend, so I quizzed him on the difference between 'refraction' and 'reflection' (and therefore got some physics in) when it came to telescopes. I hope Jared feels better soon.

We spent the whole class mulling over our current datasets, and re-calculating manually the standard deviations for all our datasets to ensure that we have the correct values. We then used these standard deviations to calculate the z-scores for all datasets, and concluded that the spike in the astronauts' birthdays in March is the most significant amongst our numbers. Jared was amazed that two disparate datasets produced the same standard deviation, an excellent example of statistics!

Following on from yesterday's class on standard deviation, today we looked at one way of showing how data values in a dataset compare to other values in the same dataset. One way of doing this is via the z score, or standardized value, which states the number of standard deviations that a data value deviates from the mean. The z score is expressed as z = (x - x_mean) / s for a sample.

We are reviewing for her exam on hypothesis testing.

Today we continued looking at patterns in birthdates, and concentrated on the early space era astronauts, those of the Mercury, Gemini, and Apollo missions. There is a definite spike for the month of March. To examine the numbers better, we manually calculated the standard deviation of the data set using both the regular method and the shortcut formula. Our manual calculations gave us the same number (and mainly, provided Jared with an understanding of how the formula works) while Excel gave us a different number. This taught us an important lesson: that before using software blindly, it is very important that the principles behind the software are fully understood. We scrutinized the formula used by Excel (in the info section), and it corresponded to the one we were using... Therefore, we must have been inputting the data erroneously in Excel. This example makes one think of how prone to error we can be when we don't understand our tools.

Today we took a look at the birthdays of the early astronauts, those that were selected for the Mercury, Gemini, and Apollo missions. Jared had started collecting that data already in the Fall, so now we're consolidating those with the other birthdates. There is a very interesting spike in the astronauts' data that we will take a closer look at in the days to come. As often in our classes, Jared asked very interesting and pointed questions, mostly about spaceflight today, but as always, I very much appreciate his curiosity.