# Difference in probability and statistics?

• vptran84
In summary, statistics is a way of measuring the occurrence of events, while probability theory is a way of estimating what might happen.
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

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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.

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 ?

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

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

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.

honestrosewater said:
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%.

## What is the difference between probability and statistics?

Probability is the branch of mathematics that deals with predicting the likelihood of future events occurring, based on past data and assumptions. It involves calculating the chances of a particular outcome or event happening. Statistics, on the other hand, is the branch of mathematics that deals with collecting, analyzing, interpreting, and presenting data. It involves using data to make inferences and draw conclusions about a population or phenomenon.

## How are probability and statistics related?

Probability and statistics are closely related as they both involve the use of data to make predictions and draw conclusions. Probability provides the theoretical foundation for statistics, as it allows us to calculate the chances of a particular event occurring. Statistics, in turn, uses probability to make inferences about a population or phenomenon based on collected data.

## What are some examples of probability and statistics in everyday life?

Probability and statistics are used in various fields and aspects of everyday life. For example, probability is used in weather forecasting to predict the chances of rain, in sports to predict the outcome of a game, and in insurance to calculate the likelihood of an event occurring. Statistics, on the other hand, is used in market research to analyze consumer behavior, in medical studies to determine the effectiveness of a treatment, and in polling to predict election outcomes.

## What are the main applications of probability and statistics in science?

Probability and statistics are important tools in scientific research and experimentation. They are used to design experiments, analyze data, and draw conclusions about the results. In fields such as genetics, physics, and chemistry, probability and statistics are essential for making predictions and understanding complex phenomena. They are also used in the development of new technologies and advancements in various scientific fields.

## What is the importance of understanding the difference between probability and statistics?

Understanding the difference between probability and statistics is crucial for accurately interpreting and analyzing data. It allows us to make informed decisions and draw reliable conclusions based on evidence and probability calculations. In many scientific fields, a strong understanding of probability and statistics is necessary for conducting meaningful research and making progress in the field. Additionally, understanding these concepts can also help individuals make better decisions in their personal and professional lives by evaluating risks and making predictions based on data.

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