Chapter 5: Stories Quantitative Data Tell, Continued (Day 33)

Today in Stats, we continue with the next three pages in Chapter 5, "Stories Quantitative Data Tell." These pages discuss how measures of center and spread are affected if each data point is multiplied or divided by a constant.

Unfortunately, the students appear to be confused by this concept. The example in the book involves converting data from kilograms to pounds -- that is, multiplying by 2.2. There is a histogram where all the weights are divided into bins of 10 kg each -- that is, 50-60 kg, 60-70 kg -- but when these are converted to pounds, they become 110-132 lbs., 132-154 lbs. and so on. These non-multiples of ten are hard to find on the histogram where the scale is marked in tens.

And this confuses the students. What should have been a simple concept -- when you multiply (or rescale) the data, all the key numbers (mean, median, mode, range) are multiplied by that constant -- is instead obscured by that strange factor of 2.2. I try to give a simpler example involves yards and feet, and thus a simpler scale factor of three -- but by this point the students look hopelessly lost.

The Chapter 5 Test is coming up on Thursday, Fortunately, the chapter is done for the most part, so I don't have a full six pages to cover tomorrow. This means that I can spend more time on non-text examples that might be easier for my students to understand. For example, I might ask questions like, "If we multiply each data value by two, does the mean change?" and "If we add three to each of the data values, does the range change?" Markers and whiteboards will fit with this kind of lesson.

The Calculus students are also struggling with their work as they prepare for the Chapter 2 Test -- but then again, their work is more difficult. Difference quotients and the limit definition of derivative are difficult for any student.

In fact, for Calculus, today is another Michael Starbird lecture. Since Lectures 3 and 4 refer to the integral, I'm saving them for second semester. So I skip directly to Lecture 5, "Visualizing the Derivative." This lesson covers some of the same material found in the last three sections of Lecture 2.

In Ethnostats, we're continuing the Global Climate Change posters. I'm trying to get the students to move more quickly, because there are other activities I found from the old Ethnostats website from two years ago and I want to begin these soon.

One guy in my fourth period Ethnostats did something interesting over the weekend -- he ran in a Cross Country race. I knew that our team would be small, and unfortunately, our XC team is as large as my old first period class -- that is, one. He ran in the Bell-Jeff Invitational -- and while he can't tell me his exact time, he says that he ran the three miles around 21 minutes. Of course, I tell him about my own days as a high school XC runner. Indeed, I ran at Bell-Jeff once in my career, also as a senior. My time that day was in the 18-minute range -- but after the race, we were told that the course was measured to be slightly less than three miles. I hope that the distance was measured correctly for our runner last Saturday.

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