Math Things - Statistics

I don't believe I've covered a stat post yet, possibly because mostly I play with imaginary numbers, and abstract concepts. *sheepish grin* Learning statistics is actually incredibly useful, although one can get caught up in the formulas and doomed to roam the bell curve forever...

Anyway, without further ado, here are some intro notes to the all-scary statistics field:

1. Animal Shelter: Collecting and interpreting data, narrowing the field.
First, statistics is essentially collecting data, then sorting the data into subsections to answer questions. Let's say you go to an animal shelter, which by the way, you should go. And adopt a puppy. Because puppies are amazing! Anyway, you go there, and they have let's say 100 cute adorable faces to choose from. Most of the time, you walk up and down the isles, barking at the dogs until you find one you like. But let us say that you want to narrow it down a little, spend more time per puppy, but only look at the kind of puppy you want. You ask the nice volunteer how many fluffy medium sized dogs they have.

They may check their database, and realize they have 60 medium sized dogs, and of those 60, roughly 12 of them are fluffy. That narrows the field. :)

2. Husky's: Finding Patterns, Estimates, and Averages.
Secondly, statistics is often used to find patterns in data, find averages, and make predictions.
Back to our animal shelter! We go looking for a husky, for example, but they don't have any Husky's. *Sob*. So, naturally we ask, "do you ever get any Husky's in?" They can look through their history, and search for Husky, and they may tell us, they have gotten in 4 Husky's in the past 2 years. That may be the beginning of a pattern. You ask them, were those Husky's one litter, or did you get them at intervals? It may turn out they a Husky in about every 6 months, and they are adopted really quickly because there are a lot of Husky lovers out there. So the pattern is 1 Husky per 6 months. It's been about 3 months since they last had a Husky, and you decide to wait 3 months and come in to check. Awesome! That's finding a pattern, getting an average, then making an estimate! Not only do you get a fluffy blue-eyed Husky in 3 months, but you were using Statistics! *High Fives*

See? This stuff isn't so bad.

3. Those Silly Marbles: Probability
If you are past grade 6, chances are you have heard the age-old question, if there are 10 marbles in a bag, 4 are green, 2 are red, and 4 are blue, what are the chances of pulling a blue marble out? Or, here is another one: You are getting dressed in the dark. You own 6 pairs of socks. How many socks do you have to grab to know you have grabbed at least one matching pair? First, I would like to ask the guy, silly rabbit that wrote this, "Why am I only pulling one random marble from the sack? Why do I have a sack of marbles? If I plan to play with them, wouldn't I dump the whole lot on the floor? And why am I getting dressed in the dark? Do I even care if my socks match? Furthermore, if I have a roommate, or spouse that I don't want to wake, what are the odds of grabbing only socks in the dark to begin with? Like most people, my sock drawer doesn't contain only socks. Obviously, the pretty math problems on paper don't tend to factor in real life examples... Let's make our own:

The Holidays are almost here. You want to bake some amazing Chocolate Chip Cookies. However, about the time you are ready to place the cookies in the oven, you notice 3 bunnies hovering over you, wanting to sample the dough. Normally, you might let them, but this time, you had just enough batter to bake 15 cookies (after you snuck a taste of course). You need 14 cookies to take to you friend's Hobbit feast party, and can only spare one. Therefore, you decide to have the bunnies flip for it. A coin doesn't have 3 sides, so to make it fair, you take a dice, and assign each bunny 2 numbers on the dice. Blue bunny gets 1-2, Gray bunny gets 3-4, and Brown bunny gets 5-6. This way, each bunny get's an even chance at the cookie. With this example, it's pretty easy to tell each bunny gets a 2/6 (or 1/3) chance of winning. But suppose Blue and Gray bunny were in you fur the whole time you were trying to make the cookies. You decide to dock each of them 1 number. Now Blue gets 1, and Gray gets 2, and Brown gets 3-6. The odds have changed:
Blue = 1/6 chance
Gray = 1/6 chance
Brown = 4/6 chance

This way, all the bunnys still have a chance, but since Brown was the best behaved, she will get a better chance at winning than the other two. I think that is a much better example of a realistic example of probability.

In general, count the total number of possibilities, then count how many winning chances each person, or outcome has. Here are a few more examples:

Suppose instead of Bunnies and cookies, you were running a raffle on a new battleaxe. You sold tickets for 3$ each, and each person was only allowed to buy up to 10 tickets. You have a total of 50 tickets, and plan to use the 150$ proceeds to actually buy the prize battleaxe, and a small hobbit-y blade for yourself.

So the total possibilities are 50 tickets, where each one could be the winner. Let's take a look at who bought the tickets, and how many they bought:


Blue Bunny:         10 tickets
Gray Bunny:        10 tickets
Luna Cat:             5 tickets
Frankenstein Cat: 5 tickets
Black kitty:            10 tickets
Husky:                  5 tickets
Meow:                  1 ticket
Story:                    1 ticket
Smitty:                  3 tickets  (not entirely sure why a car needs a battleaxe..?)
Total;                    50 tickets

So, for example, Blue Bunny has a 10/50 or 1/5 chance of winning, while Smitty only has a 3/50 chance of winning.

Suppose sheepdog was worried that a bunny might win, and his troubles would never end. What are the chances of a bunny (any bunny) winning?

What are the odds of Story winning? Do you think she would keep it or give it to her parents?

Do you think Black Kitty would win? Why or Why not?

Have Fun!
Feel free to guess who will win! I will edit later with the winner.

-SheepDog-