Besides the usual quote on the board today, I also have this math pickup line: How can I know hundreds of digits of pi and not know your phone number? I am featuring a new math love / pickup line each day this week (some days will have more than one). If you want the list, Math & Multimedia is the source.
But anyway, I hate to even call this a #180 blog posting, because I gave up on that at the semester. I just was not focused enough to maintain. I don’t know how people do it. But I do want to share some of the Central Limit Theorem Love I just did.
The exercise is not my own. I stole it from Josh Tabor and I credit him fully with the idea. What you need for this exercise are pennies, chart paper, and some fun dots. That’s it. You need a lot of pennies though. By a lot I would estimate I have approximately 2500 pennies in a bucket. I don’t know exactly how many, but it is a huge number. I emailed the staff at the school and asked for pennies and they delivered. Each year I ask for more, and they deliver more. It is terrific.
Okay, on to the set up. When the learners walked in the room, they saw this:
The instructions, the left chart paper for x’s, the middle for xbar’s and the right for p-hats. Yes, the scale is completely wrong on the p-hat chart. It should be from zero to 1. I fixed that.
Then, the learners pulled their coins, found the means, the proportion greater than 1985, and we graphed using stickers for the x’s, writing xbar and phat for the other two. At this point, we ended up with some good looking graphs. We discussed if we could tell the mean of the dates from the x graph, we decided we could not, so we OBVIOUSLY needed more data.
Do it again.
After two rounds, we ended up with these graphs:
I did change the 1985 to 1995 by the time I took these pictures from my 3rd period of Stats. The newer pennies the staff gave me pulled the mean up.
I actually tore the “Actual Values” graph down and threw it on the ground because it was so useless. That was the point of that graph. I loved how the other two graphs were so clearly unimodal and symmetric. They fit the idea of the CLT perfectly. The fact they matched was just icing on the cake!
http://onlinestatbook.com/stat_sim/sampling_dist/ Using this simulation for the CLT, we then looked at what happens when sample sizes are changed, whether the shape of the population matters, etc. It was very eye-opening.
Then we discussed the reason why, how, and what conditions must occur for one sample to then represent the population. The notes I used are here in pdf format. I am trying something for the end of the year where I post the notes before hand and they are required to read them as homework. I HATE going over the notes in class. So far it is a good experiment.
Next up are some in class problems.
This is the third time I have done this exercise, but only the second time I have used xbars and phats. It is very useful to have those there so the formulas make more sense.
The fact that the formula reads “the population mean is identical to the calculated mean of the sample” is very useful when the learners keep the population mean and the sample mean separate.