The digits came from one of Danica McKellar's books (see below).
Students observed different characteristics of the number sequences. They were making statements about what they believe this showed. My comments back to them centered on asking how they could gather evidence (data) that would either support or contradict their claim. Some were able to immediately determine a course of action using random numbers. Others needed more prompting and guidance. All realized that they needed to compare the given data set to truly random digits to see if the characteristics they were observing were present in the truly random digits.
I had students examine the ratio of odd to even numbers, the number of repeated digits, palindromes of five numbers, sandwiches (a number squeezed between two numbers of the same value), and the distribution of digits present. Two groups felt the evidence showed the data was random, three thought the data was human generated, and two groups felt the results were inconclusive.
The most compelling evidence came from looking at the counts of digits present in the random numbers. The distributions looked much more variable in the truly random sets whereas the given data showed a much more uniform distribution.
One thought that came from a student was the issue that in an infinite long series of random numbers, the given values should appear. This is true. But at the heart of statistics is how frequently should you expect to see that sequence. Is it that one in a million chance occurrence or is it a one in five or one in ten chance?
We will continue to explore these ideas as the course progresses. This investigation was their first look at true statistical analysis and the students were engaged and interested in what their data was showing. It was a good close to the week.
Visit the class summary to read a student's perspective of the class.
No comments:
Post a Comment