[OT] Averages

[randomling]

Are there any mathematicians out there who know the difference between a mean, a median and.... um... the other one? A modal, I think it's called.

And if so, could you please explain them to me in terms that a stupid person would understand? It's not homework or anything so there is no sense of cheating involved... just curious, and I've forgotten since school.

Thanks!

 

[Sir Whiskers]

Take 5 numbers: 1, 3, 3, 4, 9

Mean: also known as the average value, add all numbers, divide by the number of numbers.
1+3+3+4+9 = 20
20/5 = 4

Median: the number in the middle of the progression (in other words, there are the same number of values less than the median as there are greater than the median. Simply remove the highest and lowest values one at a time until only one value is left.
1-3-3-4-9
3-3-4
3

Mode: the number which occurs most often
1 - 1 time
3 - 2 times
4 - 1 time
9 - 1 time
Mode = 3

By the way, each term respresents something very different, which is why statistics often lie. If someone says the average annual income in a country is $5,000, but the median income is $100, you know that most of the country's wealth is concentrated at the top (half the people make $100 or less, but the average wealth is much greater, meaning the people at the top make millions). If the median and mean are close to the same, then wealth is more evenly distributed. Another example: If someone says the "average" customer has XYZ qualities (where they live, how much the make, education level, single/married, etc), do they mean average (as in "mean") or typical (as in mode)? How someone crunches the numbers changes significantly what they mean.

 

[Umbran]

Mean: average - add them all up, divide by the number of entires.

Median: the middle number in a sequence. If your numbers are sorted in ascending sequence, the median is the one in the middle of the list (or, if there's an even number of entries, it's the average of the two middle numbers)

Mode: The number in the sample that occurs most often.

 

[randomling]

Thanks! That makes lots of sense now -- I knew there were different types of average, but I couldn't remember which was which. Now I do, so, cool.

Basic statistics, here I come!

 

[randomling]

OK so here's where we hit on-topic.

When you talk about the "average" roll of, say, 4d6, are we talking about a mean, median, or mode?

 

[Octopus]

When you're taking about the probability of a dice roll, the mean is what's actually, well, meaningful. If you graphed the results of rolling 4d6, it would be a bell curve, which means the results will be about half and half on either side of the median, and also that the median is close to the mean.

 

[Mercule]

OK so here's where we hit on-topic.

When you talk about the "average" roll of, say, 4d6, are we talking about a mean, median, or mode?

Almost universally, when the "average joe" (pun intended) talks about "averages", he's talking about the mean.

I think I can count the number of times I've used mode or median in real life (i.e. not a classroom) on one hand. Granted, I'm not a mathematician, but I do tend to do more, and more complex, math than anyone in my circle of friends.

 

[Tiefling]

Incidentally, every number from 1 to 20 can be added and divided by 20 to get 10.5, and since average is generally interpreted as mean, it can be said that the average roll on a d20 is 10.5. This can be misleading if you don't know much about statistics, though, because you're equally likely to roll any number from 1 to 20. There isn't any mode in the set. This is why games like GURPS use multiple dice, so that a bell curve is established, and you're much more likely to roll an average result than one on either end of the spectrum.

 

[kingpaul]

OK so here's where we hit on-topic.

When you talk about the "average" roll of, say, 4d6, are we talking about a mean, median, or mode?

Is this before or after you drop the lowest roll when setting stats? {pun intended}

Edit Delete errant 4

 

[mmadsen]

When you talk about the "average" roll of, say, 4d6, are we talking about a mean, median, or mode?

The mean, median, and mode of a multi-die roll are the same -- at least if you ignore rounding issues. It's a "normal" distribution.

On 4d6, the mean is 14 (4 x 3.5), the median is 14 (half the time you roll less, half the time more), and the mode is 14 (there are more ways to roll 14 than any other number).