Statisticians, analysts, researchers, etc. use interval estimates in a formal way to evaluate data. However, it's a bit more interesting to think of how the rest of us use them in an intuitive and informal way. In doing so we will hopefully learn a bit more about why the formal use is important.

Here is a useful and informal example of how our brains naturally prefer ranges (intervals) of numbers (as opposed to a single number, such as a guess at the average) to "estimate" problems in our lives: At some point, you have to make a decision about what to major in during your time at school. One major component of this choice is salary. Lots of majors like to present the average salary of their graduates as a way to attract students. For instance, see this article.In that study, they find that Finance majors have an averagestarting salary of $58,000.However, this single number really doesn't give a prospective student much information. Average really doesn't say much about what youwill actually earn - could be more, could be less. A better piece of information (and one our brains naturally tend toward) would be if someone told prospective Finance majors that they can be fairly certaintheir starting salary will be between $50,000 and $66,000. This is an example of an informal interval estimate in action. (Note: If we were to formally estimate it we might say something like "we are 95% confident that a Finance major's starting salary will be between $50,000 and $66,000)

1. What I would like you to do is come up with a situation or example where thinking in terms of an interval makes a lot of intuitive sense. In a few sentences explain your scenario and why an interval gives us more information than a simple average. I'll give the early movers an advantage and provide some hints at places where this should be intuitive for students: grades, how long it will take you to get somewhere (or what time you arrive), how good you are at Modern Warfare, etc.