The mean, median, and mode tell different things about the middle of a data set. Comparison of data from two groups should involve comparing both their middles and the spreads around them. The larger a well-chosen sample is, the more accurately it is likely to represent the whole. But there are many ways of choosing a sample that can make it unrepresentative of the whole. Events can be described in terms of being more or less likely, impossible, or certain.
Students construct a shadow tracker.
After using a compass to orient the shadow tracker north, the students make hourly records of the position of the tip of the shadow cast by a golf tee. After the recording has been completed, students look for patterns in their tracking log. If people have rules that always hold, and good information about a particular situation, then logic can help them to figure out what is true about it. This kind of reasoning requires care in the use of key words, such as if , and , not , or , all , and some . Reasoning by similarities can suggest ideas but can't prove them one way or the other.