This is one of an occasional series of mondo-tough problems that use small numbers (or no numbers at all!) Here’s how it works: we all teach our students how to take a group of numbers and calculate the range, mean, median and mode. Seems pretty simple, and our students tired of it damned quickly. Can you blame them? It’s just “do what the teacher told me to do, and then write the answer here...” kind of busywork.
But what if we were to switch the tables on our students: let’s give them the statistics, and they have to figure out what the data looks like to fit those statistics? Sounds hard, right? Well, it is, and it isn’t, because if your students really know their stuff, they should be able to solve it, right?
So what we’ve got here are two sets of statistics: one tells us about the measures of 5 different water glasses, and the students have to figure out how to fill the glassses with different amounts of water in order to get it to conform to the statistics. The numbers are not that difficult, and the are all under 10. Could you make it much easier?
The second problem is almost the same as the first, but this time it is the ages of a group of suspects in a case. Again, we have the mean, median, mode and range, but the job of the student is to figure out what the ages of the 5 different suspects could be to get this set of statistics.
You may say, well, there should be an infinite amount of answers, but if you use whole numbers (which I encourage you to tell your students, or they’ll go nutes....) you would be surprised that there are not that many solutions to the first problem (2) and more on the second (9.) If you find more, I’d be happy to publish them.
If you look at this, trying to get the mean, mode and range to work won’t be much of a problem, because those are pretty easy to figure out because they don’t involve much in the way of a calculation (except for the range, which requires subtraction.) It’s the mean that’s going to get your kids hung up, but if you read the following paragraph, you’ll see that it won’t be all that hard.
(but you'll have to buy this activity to find out "how to cheat the mean!")