From Maura
The main objective today was to understand histograms. I told them that these graphs are useful for understanding the distribution of data, especially when you have a lot of data. We pulled up the Wing Aero spreadsheet again and used the groupings that were already there ($0 to $20,000; $20,000 to $40,000; etc) and had Excel count the frequencies in each group, then made the graph. Then we talked through what we could see from the graph and what that told us about salaries for the company.
My hope is that by building a histogram, they build their understanding of what a histogram is. But reading a histogram is really what we are getting at, so we also looked at an example without the distractions of Excel. We looked at the population pyramid from France for 2011. It’s a histogram turned on its side so that gender data can be displayed. We talked through the basics (what is being measured, what are the units, etc) and then made a list of observations about the distribution of ages. In the long run, reading histograms will be the important skill for these students. The more practice in this, the better.
Our last exercise was to go back to the Wing Aero grouped data and use Excel to calculate the mean and median. We had to pretend we didn’t have the original data and instead use the groups and the frequencies to estimate the mean. This is a very useful exercise and they will have several opportunities to practice it in the homework.
From Ethan
I started the class with a mock tirade about not thinking: averages larger than all the numbers being averaged, 10% raises turning into 20% raises after 2% inflation, … . I recommended writing something like “The answer I just computed makes no sense. I don’t know what I did wrong, but this can’t be right” as a way to prove that you’re thinking, even though you’re stuck or confused. It not by accident that the text is called Common Sense.
The real work of the class was on histograms. Students’ prejudices about which average to use lead them to mean-median-mode, but looking at grouped data (a table or a histogram) reverses that order).
Computing the median and then the mean from summarized Wing Aero data provided opportunities to show how Excel changes cell references when you paste formulas in new locations. We even ended with a computation where we didn’t want Excel to increment a row index, so introduced the cell reference E$18 to replace E18.
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