We are going through her teacher's review questions for her final exam.

in wrapping up this year's work, we looked again at the formula for the standard deviation of a data set, and more importantly how to use it. The standard deviation describes exactly what it says: by how much each element in the data set deviates from the mean of that data set. Jared worked through an example on the board, by first identifying the steps required to perform the calculation, i.e. finding the mean of the data set, the difference between each element and the mean, the square of each of the latter, the sum of the squares which is then divided by the number of elements, and the square root of all this.

Continuing on from our work on box-and-whisker plots and quartiles, today we analyzed four data sets in terms of their median, mean, and mode. The data sets all had the same measures of center, even though the actual numbers in the sets differed. The lesson to take away here is that measures of center (such as the median or the mean) don't necessarily describe a data set fully, they only give a handle on what value the numbers cluster about. A way to understand better the spread of the data set is to evaluate the first and third quartile, and determine the interquartile range (essentially, the difference between the third and first quartiles) - a smaller number indicates less spread, while a larger number indicates more spread.

Jared had worked quite hard on revising his answers on yesterday's test, so I thought it might be nice for him to end the week with a stimulating documentary. We browsed together through the PBS Nova archive, and pulled up a documentary on Einstein's thought experiments that eventually led to his theories of Special and General Relativity. As always, I paused the video often to discuss certain mathematical or physical principles that were discussed. And as always, Jared was riveted, and asked very relevant questions.

We continued with a few examples of the box-and-whisker plots and discussed how they provide immediate visual cues as to how the dataset is distributed. We moved on to the concept of outliers, and discussed the various origins of outliers (true data points indicative of anomalous behavior, or erroneous data points due to a variety of factors, including human error, data processing errors, etc). We then studied a couple of examples of deriving the measures of center with outliers, excluding obvious outliers, and comparing the two.

In starting to wrap up this year's work, today we revisited measures of center. These include the mean, median, and mode(s) of a dataset. Jared is very familiar with this topic, so we were able to proceed quickly through the material. We also looked at producing a 'box-and-whisker' plot for a dataset from its quartiles. Quartiles are derived from a dataset by initially identifying the median, and then finding the medians for the resulting two halves. The range covered by the medians together with the maximum and minimum values of the dataset form the box-and-whisker plot, which is one useful way of visualizing the data.

We worked on Jared's homework problems in class today. We reviewed the idea behind probability trees while working through one of the problems, and then dissected two word problems so as to understand how the information given verbally can be transformed into numbers using the well-known formula for conditional probabilities, i.e. P ( B | A ) = P ( A and B ) / P ( A ). The left-hand side of the equation translates to 'the probability of event B happening given event A'. The math is always rather straightforward, it's interpreting the problem that is trickier.

We went through the first part of her review packet for her test tomorrow: Goodness of Fit Test and contingency tables.

We worked on her test review worksheet covering ANOVA, F-tests, p-values, and their interpretations.

We continued studying probability trees in today's class, paying specific attention to the nature of the various branches. The first branch represents a simple probability, and the second branch represents the conditional probability of the situation. In other words, the subsequent branches are dependent on the states of the first pair of branches.