Year 8s I want to see how many of you can follow Lyn’s advice on how to move your blog and all your posts. I am copying her instruction so that you can follow them. If you don’t have an email account of your own at home you will need to do this at school using your school email.

I am also moving this blog but it won’t happen until the weekend. Can you beat me to set up your new blog? I might even have something for anyone who gets their blog setup before me!

Lyn’s Instructions

The overwhelming majority of us were taught how to round decimals back in either elementary or middle school. (I don’t even recall exactly when.) The rule that most of us were taught is:

1. If the first digit after the rounding point is 0, 1, 2, 3, or 4, then round the previous digit down;
2. If the first digit after the rounding point is 5, 6, 7, 8, or 9, then round the previous digit up.

Here’s the problem: those rules are wrong.

The problem is that if the first digit after the rounding point is zero, you’re not really rounding - that is, you’re not doing anything that changes the value of the data point. But if the first digit after the rounding point is 5, then it’s exactly halfway in-between; it’s not closer to the either the rounded up value or the rounded down value - it’s exactly between them. Always rounding 5 up will create a bias, because it’s taking the point at the middle, and shifting it as if it were closer towards the upward side.

To demonstrate, let’s try an easy example. Suppose we’ve got the following set of numbers: {0, 0.5. 1, 1.5. 2, 2.5, 3, 3.5, 4, 4.5}. Let’s compute the mean of those numbers: 22.5/10 = 2.25.

Now, let’s round them off: {0, 1, 1, 2, 2, 3, 3, 4, 4, 5}; and then compute the mean: 25/10 = 2.5.

With the standard rounding rule, we’ve biased the numbers upwards enough to create a significant error!

The correct way to round is to randomly round 5s either up or down. The standard rule, used in most scientific settings, is to pick either odd or even as the “preferred” outcome, and to always round 5s towards the preferred outcome. If we try that with our example, using preferred even, the rounding is {0, 0, 1, 2, 2, 2, 3, 4, 4, 4}. Taking the mean of that, we get 22/10 = 2.2 - which is significantly closer to the mean of the original numbers than the mean rounding 5s up. The practice of rounding up adds a systematic bias to the data. It’s a very small systematic bias, but it’s a real one.

Does it matter? Not usually. As the commentary to the video points out, over the space of a couple of years, that systematic error in rounding gas prices amounts to about a dime. For most things in our daily experience, the difference between random rounding and upward rounding for 5s is just not significant. But if you’re doing statistical analysis of large quantities of data, or you’re doing computations that rely on a high degree of precision, then it can introduce enough error to foul your results. If you’re doing statistical analysis, it can do things like make an insignificant result appear to be statistically significant. If you’re doing high precision computations for things like navigation of a space probe through a gravitational slingshot, it can introduce enough error to crash your probe.

Thoughts and comments please!

Savethewords is a great web2.0 site for good spellers. The words call out to you to pick them, and once you ‘adopt’ a word you promise to use that word in conversation. A great way for your top spellers to increase their vocabulary and have fun doing it.

The Net Generation Has Arrived.
Are you ready for it?
Chances are you know a person between the ages of 11 and 30. You’ve seen them doing five things at once: texting friends, downloading music, uploading videos, watching a movie on a two-inch screen, and doing who-knows-what on Facebook or MySpace. They’re the first generation to have literally grown up digital–and they’re part of a global cultural phenomenon that’s here to stay.

Are you part of this? Why or Why not?

Download it here

Authored by Lynne Crowe. Hosted by Edublogs.]]> http://room3tai.edublogs.org/2009/03/scorched-3d/feed/ http://room3tai.edublogs.org/2009/03/dots/ http://room3tai.edublogs.org/2009/03/dots/#comments Sat, 07 Mar 2009 05:33:41 +0000 Lynne Crowe http://room3tai.edublogs.org/?p=330 Here’s a strategy game for you to play against the computer!

Dots

Are you familiar with everything mentiones? What is your skill level with each tool? Comments please!

Check these ones out:

GIMP

Krita

Paint.NET

ChocoFlop

Cinepaint

Pixia

Pixen

Picnik

Splashup

Adobe Photoshop Express

Let us know if you find anything useful.