Difference in probability and statistics?

[vptran84]

Hello,

Just wondering what's the difference between probability and statistics? I can't seem to grasp the concept of it, can someone please explain the difference to me in Lehman's term? Also can someone give me an example of each? thanks in advance

 

[honestrosewater]

I think the distinction you want is that probability theory is pure math, while statistical theory is applied math. Statistics is the application of probability theory to the real world; It's a science, like physics, where you gather data, perform experiments, make predictions, and so on. So just as a physicist might use calculus to predict the path of a moving object, a statistician might use probability theory to predict the weather.

 

[kleinwolf]

Let suppose you have a balanced coin...The probabilities are given before (a priori datas) as p(head)=1-p(tail)=.5

You throw the coin 5 times : you get : h,h,t,t,h

The statistics are : s[h]=3/5=.6, s[t]=1-s[h]=.4=2/5

The not-always-admitted assumption of prob. theory is that p(h)=limit s[h] when the number of trials for s[h] goes to infinity.

(Now of course you can make a MODEL, where the probabilities depend on the statistics...but this is no more axiomatic prob. theory, but just a toy model.)

Since the statistic is based on an experimental data, why should this limit exist for example ? In fact this question is not even possible, since no experiment allow to throw an infinite number of time.

But also consider a mathematical example : $$X(n)=\left\{\begin{array}{cc} h & \textrm{if the nth decimal of } \pi\textrm{ is n mod 10}\\ t & \textrm{ else }\end{array}\right.$$

Does the limit exist ?

 

[vptran84]

i think i understand what you guys are saying...thank you for your responses.

 

[tonym144]

Simply put, probability deals with what SHOULD occur, statistics deals with what HAS occurred. It's simply a matter of when.

 

[HallsofIvy]

In a certain sense, probability and statistics are opposites. Probability starts from a given probability distribution, with given parameters, and gives the chances that a specific outcome with happen. Statistics start with specific outcomes (the sample) and gives the parameters for the probability distribution.

 

[moonman239]

I think the distinction you want is that probability theory is pure math, while statistical theory is applied math. Statistics is the application of probability theory to the real world; It's a science, like physics, where you gather data, perform experiments, make predictions, and so on. So just as a physicist might use calculus to predict the path of a moving object, a statistician might use probability theory to predict the weather.

Seconded.

As another rough example, let's say I roll a 6-sided dice 20 times.

Probability theory says that a 4 should happen only about 3 times (3 1/3 times, to be exact).

The statistics of the dice rolls say that a 4 actually happened 3 times (FYI, you will rarely if ever have a 4 showing up 3 times in 20 rolls.)

Statistical theory tells me that, at a 68.26895% confidence interval, the actual probability of a 4 is between 6.66666667% and 23.333333333%.