Majority of students are still not able to distinguish between probability vs statistics. Probability and statistics are the related areas of mathematics. We use them for analyzing the relative frequency of events. But there is a vast difference probability vs statistics. Let’s start with the basic comparison

Probability deals with the prediction of future events. On the other hand, statistics are used to analyze the frequency of past events. One more thing probability is the theoretical branch of mathematics, while statistics is an applied branch of mathematics.

Both of these subjects are crucial, relevant, and useful for mathematics students. But as a mathematics student, you should know that they are not the same. There can be a lot of similarities between them, but they are still different than each other.

You should see the difference because it will help you to interpret the relevance of mathematical evidence correctly. Lots of students and mathematicians do not get successful all because they were not able to find the difference between probability vs statistics. Let’s dig into the differences based on a few points:-

**Probability vs Statistics**

**Definition**

**Definition of Probability**

It is the branch of mathematics and analyzes the random phenomena that the event will occur. The outcome cannot be determined before the event occurs. But there are always several possible outcomes.

Probability is all about analyzing the actual outcomes. It lies between 0 and 1. Where 0 stands for impossibility and 1 stands for certainty. The higher the number of probability close to one, the more chances that the event will happen.

### Definition of Statistics

Statistics is a branch of mathematics. It is used quantified models and representations for a given set of experimental data. Statistics is having lots of methodologies to gather, review, analyze, and draw conclusions from any collection of data.

In other words, it is used to summarize a process that is used by the analyst to characterize the data set. Statisticians use statistics analysis for gathering and evaluating data. It is also used to summarize the data into mathematical form.

## Examples

### Example of Probability

In the case of probability, the mathematicians would see the dice and think that “Six-sided dice? They will also get a prediction that the dice will likely to land, and each face will equally face up. After that, they will also assume that each face will come up with the probability ⅙.

### Example of statistics

On the other hand, the statistician will assume the same dice scenario with different assumptions. In this case, the mathematicians will see the dice and think that “Those dice may look OK, but how do I know that they are not loaded?

For this, he will use the methodology to watch a while and keep track of how often each number comes up. Then he will decide that observations are consistent with the assumption of equal-probability faces. Once he will gain confidence enough that the dice are fair.

## Types

### Types of probability

**There are 4 significant types of probability**

#### Classic Probability

It is the first probability approach. In this approach, we often use the coin tossing and rolling dice. We calculate the results by recording all the possible outcomes of the activities and record the actual occurrences.

Let’s understand it with a solid example if you are tossing a coin. Then you will always have only two possible outcomes, either heads or tails. But if you toss the same coin 10 times, then you will have 20 outcomes, and you will record each outcome every time.

#### Experimental Probability

It is different than the recent one experimental probability is based on the number of possible outcomes by the total number of trials. For example, when we toss a coin, the overall possible outcomes are two, either heads or tails. On the other hand, if the coin is flipped 100 times and it lands on tails 30 times. Then the theoretical probability is 30/100.

#### Theoretical Probability

Theoretical probability is an approach that is based on the possible probability of the possible chances of something will occur. For example, suppose that we have dice and we want to know its theoretical probability that it will land on the number “3” when we roll it.

In dice, there are always 6 possibilities because a dice has 6 numbers. So if we want the dice land on the three number, then you have 1:6 chance of it landing on 3.

#### Subjective Probability

Subject probability is also known as personal probability. Because it is based on a person’s own personal reasoning and judgments. In other words, it is the probability of the outcome that a person is expecting will occur. There is no formal methods or calculations for subjective probability.

Because it is based on a person’s knowledge. For example, suppose that you are watching a football match. And during the match you the home team will win the match. Your decisions may be based on facts or opinions regarding the game of the two teams and also the likelihood of the team winning.

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### Types of statistics

#### There are two types of statistics

#### Descriptive

In descriptive statistics, the statistician describes the goal. In this, we use numerical measures to tell about the features of a set of data. besides, the descriptive statistic is all about presentation and collection of data.

It is not as simple as it appears to statisticians. The statisticians need to be aware of designing experiments, choosing the right focus group. They should also avoid the biases to get more robust results from the experiments. There are two types of descriptive statistics.

#### Types of descriptive statistics

- Central tendency measures
- Variability measures

### Inferential Statistics

Inferential statistics is not easy statistics. It is more complicated than descriptive statistics. It is produced through complex mathematical calculations. These calculations are quite helpful for scientists.

And allow them to infer trends about a larger population based on a study of a sample taken from it. Most predictions of the future are made with the help of inferential statistics. Statisticians need to design the right experiment to draw the relevant conclusions from his study.

#### Types of inferential statistics

- Regression analysis
- Analysis of variance (ANOVA)
- Analysis of covariance (ANCOVA)
- Statistical significance (t-test)
- Correlation analysis

## Model

### Probabilistic Model

We use this model to incorporate the random variables and probability distributions into the model of an event or phenomenon. We know that the deterministic model provides only a single possible outcome for an event.

While the probabilistic model, we have a solution in the form of the probability distribution. These models are beneficial because they aware us from everything about a situation that we may miss without these models.

Here is an example, suppose that you have life insurance. That is based on the fact with certainty that you will die. But you don’t know when you will die.

### Statistical Model

A statistical model is a kind of mathematical model. It includes the set of statistical assumptions concerning the generation of sample data. It represents the data in an idealized form and the data-generating process.

Statistical modal also specified as a mathematical relationship between one or more non-random variables as well as random variables. Statistics model has also derived all statistical hypothesis tests and all statistical estimators.

## Uses

### Uses of Probability

Probability has something to do with every change you may create. In other words, it is a study of things that something might happen or not. Probability is a crucial part of our life.

We use it many times in a single day without thinking. We use it most of the time, usually without thinking about it. Everything from the weather forecasting to our dying chances in an accident all is the probability.

- Probability helps us to get an idea about the weather forecast. In this, we select some of the forecasting condition and then apply the probability to eliminate the one which has more chances to happen.
- It is also helpful in cricket. Do you know how? It helps in getting the estimate batting average of the batsman. Let me explain it with an example whenever a batsman comes out to the cricket field for its batting. The statistics analyze its average based on the matches it played. It also counts the match he is playing and calculates the average on the basis that it will be no out in this match.
- It is quite useful in Politics. Don’t you know how? Success in political elections is based on the number of different things. Probability helps us to get the estimation from these factors individually and combined to estimate the most deserving candidate to win.
- Probability is always helpful in flipping a coin or dice. We use both of these in various situations. Probability always let us know how many times the particular event can happen.
- It is also helpful for insurance. There are various kinds of insurance. And all insurances are depended on multiple factors. Probability helps the company to calculate how many chances that insurance holders have to claim the insurance.

### Uses of Statistics

Statistics keep us informed and alert about what is happening all around us. Statistics is a crucial part of our life because our world is full of information. And all this information is determined mathematically by Statistics Help. It means that statistics are helpful to get correct data. Here are the several uses of statistics in our daily life.

- Research is impossible without the help of statistics. Because statistics offers various methods that help the researcher to do research more effectively, they use their statistical skills to collect relevant data from multiple sources. And then perform some statistics methods on the data to get to the conclusion.
- Statistics is also helpful in the financial market. It plays a crucial role for investors and traders. It helps them to calculate which share or bond has more market value. Based on statistics, they make their investment strategy.
- Statistics also has its importance in the field of medical science. The scientist shows a scientist must show a statistically valid rate of effectiveness of the drug. It also helps in determining the effect of any disease among humans and animals.
- Every industry is using statistics daily to perform various operations. One of the major concepts for every industry is quality testing. Every company makes many products daily. And they also do not want to compromise on quality. The company can’t test every single product. For this, they use statistics sample to check the quality test of the entire batch.

## Conclusion

Statistics and probability are significant parts of mathematics. But as statistics students, you need to know the difference between these two terms. There are lots of similarities between these two. But it is a lot different than each other.

Now you may be sure about the difference between probability vs statistics. So get ready with the answer whenever someone is going to ask the difference between probability vs statistics.

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**What is Probability?**

It is the branch of mathematics and analyzes the random phenomena that the event will occur. The outcome cannot be determined before the event occurs. But there are always several possible outcomes.

**What is Statistics?**

Statistics is a branch of mathematics. It is used quantified models and representations for a given set of experimental data. Statistics is having lots of methodologies to gather, review, analyze, and draw conclusions from any collection of data.

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