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!

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?

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

Let us know if you find anything useful.

The eyeballing game

The Eyeballing Game is an interactive visual estimation game. In the Eyeballing Game players are presented with a drawing or a line segment, angle, or shape. Players are then given a task like “find the spot equidistant to all sides” or “bisect the angle.” From Mr Bryne at Free Technology for Teachers

What do you think of the ideas in this clip?


When kids at the Suffern Middle School were asked to talk about education and their future, they gave Peggy Sheehy, the SMS media specialist, an earful. Listen and learn the bits of wisdom that can be gleaned from the students, if we only dare to ask them.

Microsoft has put together a concept video showing what the world could look like in another 10 years. The Future Vision Montage shows a world where face to face communication is easier thanks to video walls that let students in the US interact with children across the globe with no language barriers. And it shows a world where computers and software make it easier to collaborate, share ideas, and carry your information with you at all times.

What do you think? Is this your future?

Fairfield Intermediate : Home (Hamilton, New Zealand)

This is the school where Erin Freeman is teaching, there are five classrooms which are student BYOL (students bring their own laptops to school) – very progressive, this is the first school I’ve ever heard about which is following this model

more fromwww.fairfieldintermediate.school.nz

My thoughts: Why aren’t we doing this? I have tried but there seem to be too many stumbling blocks. Why can Fairfield do it and not us?

What do you think about having laptops? Would your parents be prepared to buy you one to use at school ( & home)? I am really interested in your comments.

Did you see this on Close Up?  No, you were probably having tea with your family, practicing music or sport.

This video clip on TVNZ’s website is about kids at Pt England School in Auckland. Check out what they are doing with ICT and ask yourself some serious questions about why we aren’t doing this. We started to get there a few years ago when Hamish was in our class but nobody seems prepared to tak on the challenge. Any takers?