A few years ago, I came across this one on Dan Meyer’s blog. It’s from 2007, so it has been around for a while. I’ve been using it in Math 20-2 classes to adress mean, median, mode and standard deviation. Here’s my approach.
Create a PowerPoint or Notebook or Keynote file that had photos of celebrities of a wide range of ages. It works out nicely if you have one celebrity per student in your class, but if you have a class of 40, it would get a bit ridiculous. Give your kids a blank chart like this one, on which they can record their guesses as you run through the PowerPoint.
Run through the PowerPoint that has the celebrity names and photos, and ask the students to jot down the celebrity’s name and make a guess as to each celebrity’s current age. Make it competitive. Tell them there is a fabulous prize for the “Best Guesser”. Be vague if they ask you to define “Best Guesser”. This is my most recent PowerPoint.
Continue through the answer portion of the PowerPoint, and ask students to mark their own answers.
Ask the class who has the most right, and act like you are going to give a prize to that kid. Inevitably, someone will stop you with a comment something like, “Wait! I only had 2 right, but I was really close on all the rest.” Let the class discuss how best to determine the winner. They will likely come up with a formula whereby they find the average difference each of them was from the actual answer. They will likely talk about whether or not it matters if they were 5 above or 5 below or just 5 away. Award the prize.
Let them calculate their average differences from the actual answer. Now you can define standard deviation for them. Standard deviation is a tough concept for Math 20-2 students, and this activity will help them picture it as an average difference from the mean.
Show them how to find standard deviation on their calculators (Math 20-2 students do not have to do this by hand).
Now ask them which celebrity they were best at guessing as a class. Assign each student a celebrity. That student must collect all the guesses that were made for that celebrity and calculate the mean, median, mode and standard deviation of the guesses for that celebrity. Put a giant chart on the board that has headings as shown below.
Get each student to fill in the calculations for his/her celebrity. Sit back as a class and look at all the data on the board, and decide which celebrity they were best at guessing. Have a class conversation around questions like: Is mean, median or mode the best one to use to determine which celebrity we were best at guessing? What does the standard deviation tell you? Does the one with the lowest standard deviation mean that was the best guessed age? When would that be true? When would it not be true?