IPS - Day 44

Today we tackled several topics. The class started off looking at graphs for the name ranking data that was collected last class. I had asked the class to try to make a graph representing the ranking distributions. Unfortunately most of the class was unsure how to proceed on this task.

One student had prepared a histogram and another student had created a stem-and-leaf plot. We looked at the histogram first. It was well constructed. I talked about differing bin sizes and the ability to easily manipulate bin sizes using a graphing calculator.

The main focus as we looked at the histogram was to understand the distribution of the data set. I wanted students to start thinking about the big picture of what the entire data set tells us versus focusing in on a single value.

With the stem-and-leaf plot, the student used 10's as the stem. It was another well constructed graph with just a couple of minor issues. A key wasn't included, so I was able to point out that a key was absolutely necessary on this type of plot so anyone reading the graph would understand how to interpret the values. The other issue was the proper way to plot a value of 149. The student instinctively knew that this value was not plotted correctly, as the 49 was placed as a leaf on the 10 stem. In this instance, it was an easy fix to continue the stem values up from 10 until there was a stem of 14, representing 140. The leaf of 9 would then denote a value of 149.

I rotated the graph and showed that a stem-and-leaf plot was just another form of a histogram that displays our data distribution. In this case, the bin sizes were 10 units. Overall, the shape of the stem-and-leaf plot and the histogram were the same: unimodal, skewed to the right, with one or two possible outliers.

I then walked students through the construction of a box plot. I had to cover the interquartile range (IQR) as only three students were familiar with this measure. I explained how to find the 5-number summary of a data set and calculate the IQR. I emphasized that, in statistics, ranges were single values not starting and ending values. I discussed how to find the "fences" in a box plot that define the border beyond which outliers fall. Basically, any values 1.5 IQRs above the third quartile or below the first quartile are considered outliers. A label of extreme outlier is reserved for values that are three or more IQRs away from either the first or third quartile.

I then had students practice creating a box plot for the name rank data. This went remarkable well and students posed many good questions to help clarify the meaning of various values and calculations.

Next, I passed out the analysis and report requirements for the car data report. Apparently my substitute never showed the class the report requirements. I told students that this report would become a mentor text, basically a model, for a sound statistical analysis. I presented the over-arching theme of statistical analysis as I stepped through the requirements. The statistical analysis process is what we will be conducting from this point forward. We will add upon the tools we make use of to understand and interpret randomness, but the basic premise of the analysis process is now set.

Finally, I asked students to consider what other questions they could pose about the name data we collected. This discussion is intended to spur the class' thinking about questions of interest. This turned out to be a productive discussion that considered different aspects of the data collected.

Finally, we concluded by discussing responses to additional questions on the name investigation sheet. This lead to revisiting what constitutes an observational study versus an experiment versus a survey. What does it mean to ask which name is most common? Does this refer to the frequency within the class room or does it refer to the name with the most popular ranking.

All-in-all the discussion was thoughtful and a good portion of the class verbalized their thoughts.

We will be looking at observational studies in a little more depth and then move on to conducting an experiment.

Visit the class summary for a student's perspective and to view the lesson slides.