[Min T.]

Originally Posted by Doctor Elect

Let's say x is a whole number.Do you round x.5 up or down. Pick a side. We're at war.

Depends. Odd or even?

[SonOfCthulhu]

Wiki's skinny on the "Round-to-Even" method:


Round-to-even method
This method, also known as unbiased rounding, convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, elitist rounding, or bankers' rounding, exactly replicates the common method of rounding except when the digit(s) following the rounding digit starts with a five and has no non-zero digits after it. The new algorithm becomes:

• Decide which is the last digit to keep.
• Increase it by 1 if the next digit is 6 or more, or a 5 followed by one or more non-zero digits.
• Leave it the same if the next digit is 4 or less
• Otherwise, if all that follows the last digit is a 5 and possibly trailing zeroes; then increase the rounded digit if it is currently odd; else, if it is already even, leave it alone.

All rounding schemes have two possible outcomes: increasing the rounding digit by one or leaving it alone. With traditional rounding, if the number has a value less than the half-way mark between the possible outcomes, it is rounded down; if the number has a value exactly half-way or greater than half-way between the possible outcomes, it is rounded up. The round-to-even method is the same except that numbers exactly half-way between the possible outcomes are sometimes rounded up—sometimes down.

Despite the custom of rounding the number 4.5 up to 5, in fact 4.5 is no nearer to 5 than it is to 4 (it is 0.5 away from both). When dealing with large sets of scientific or statistical data, where trends are important, traditional rounding on average biases the data upwards slightly. Over a large set of data, or when many subsequent rounding operations are performed as in digital signal processing, the round-to-even rule tends to reduce the total rounding error, with (on average) an equal portion of numbers rounding up as rounding down. This generally reduces upwards skewing of the result.

People use round-to-even rather than round-to-odd as it reduces rounding to a final digit of 5, and so reduces the likelihood of error resulting from double rounding.

Examples:

• 3.016 rounded to hundredths is 3.02 (because the next digit (6) is 6 or more)
• 3.013 rounded to hundredths is 3.01 (because the next digit (3) is 4 or less)
• 3.015 rounded to hundredths is 3.02 (because the next digit is 5, and the hundredths digit (1) is odd)
• 3.045 rounded to hundredths is 3.04 (because the next digit is 5, and the hundredths digit (4) is even)
• 3.04501 rounded to hundredths is 3.05 (because the next digit is 5, but it is followed by non-zero digits)

<A id=History name=History>

[edit] History

The Round-to-even method has served as the ASTM (E-29) standard since 1940. The origin of the terms unbiased rounding and statistician's rounding are fairly self-explanatory. In the 1906 4th edition of Probability and Theory of Errors [1] Robert Woodward called this "the computer's rule" indicating that it was then in common use by human computers who calculated mathematical tables. Churchill Eisenhart's 1947 paper "Effects of Rounding or Grouping Data" (in Selected Techniques of Statistical Analysis, McGrawHill, 1947, Eisenhart, Hastay, and Wallis, editors) indicated that the practice was already "well established" in data analysis.

The term Dutch rounding originated during the Dutch Golden Age. This period of wealth was characterized by opulent feasts where many prominent Dutchmen grew round. The origin of the term bankers' rounding remains more obscure. If this rounding method was ever a standard in banking, the evidence has proved extremely difficult to find. To the contrary, section 2 of the European Commission report The Introduction of the Euro and the Rounding of Currency Amounts [2] suggests that there had previously been no standard approach to rounding in banking, and specifies that "half-way" amounts should be rounded up.

[kavorca]

See, I knew I wasn't crazy. SoC's dissertation says the same thing. You can't always round up as that will throw a bias into it. You have to round up half the time and down the other half, thus you pick a method that will do this.

[Kudama]

Awesome!

[Doctor Frankenstein]

Originally Posted by Kudama

Awesome!

Everything is awesome! Awesomeness here! Awesomeness there! Awesome, awesome, awesome! AWESOME! *pant pant pant*

[Ryan J.]

I love how quick ignorant people are to answer and then say an educated answer is incorrect. In science and statistics a better formula for rounding is used as not to create a bias. If you are dealing with large amounts of data and rounding is needed, by rounding up when the significant figure is followed by a 5 a bias will be created and the results will not be accurate. 5 is in the middle. It is no closer to 10 than to 0 and choosing to only round up is a faulty method. For strictly mathematical purposes it really would not matter. Just like it is only in science mathematics that we consider 3, 3.0, 3.00, an 3.000 to be completely different numbers. The type of rounding than a number of people demonized is called unbiased rounding, convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, or bankers' rounding. For an interesting perspective on this rounding system and how it pertains to our daily lives check out the video on the link. It is about all of the money the oil companies are able to cheat us out of by using the 3rd grade method of always rounding up if there is a five. The site will also go into some detail on the subject.

http://scienceblogs.com/goodmath/200...g_and_bias.php

[LocoPopo]

Rounding is for weaklings.

Real men truncate.

[Ma Ninja]

Originally Posted by wirthling

I was once taught about rounding as kavorca describes. Unfortunately I cannot remember the context. I think the idea behind it is that all the rounding ups of .5s can accumulate into something significant, so you mitigate that by rounding half of the .5s down. Or some such shit.

We do something similar when auditing, but never really adhered to any rule about when to go up or down. Even if you did just round them all up, the difference is likely going to be immaterial in regards to the balances we deal with.

[Ma Ninja]

Originally Posted by Ryan J.

http://scienceblogs.com/goodmath/200...g_and_bias.php

Heh, I remember reading this blog post.

[CueP]

If I owe you then it rounds down.

If you owe me then it rounds up.

[zanzabee]

I hate math.

[TeamCanada]

Up.


Zero means absolute zero imo.

[SpasticNed]

Originally Posted by Ma Ninja

We do something similar when auditing, but never really adhered to any rule about when to go up or down. Even if you did just round them all up, the difference is likely going to be immaterial in regards to the balances we deal with.

Granted I'm not putting men in space or anything, but we don't follow this method either in our data analysis. If there was any hint of concern of bias being introduced because of rounding up exclusively, I think we'd keep more significant digits rather than losing data that is proving to be influential.

[blogging sailor]

Depends on the context. Would you round a batting average of .5 to 1 or 0? Obviously neither. It's .500 biatch!

[Eat the Meat]

Originally Posted by blogging_sailor

Depends on the context. Would you round a batting average of .5 to 1 or 0? Obviously neither. It's .500 biatch!

thanks for that brilliant insight!