Probability vs Statistics: Which One Is Important And Why?

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 between probability and 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 important thing is that 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

Statistics is a branch of mathematics. It is used to 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.

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.

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.

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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.

Also Read

Types of statistics

There are two types of statistics

Descriptive

Descriptive statistics provide brief overviews of the data sample and its measurements, which aid in describing and explaining the features of a particular data set. Among descriptive statistics, center measures are the most popular.

As an example, a data set can be defined and described using the ubiquitous terms in mathematics and statistics: mean, median, and mode. To get the average or mean, you add up all the numbers in the dataset and divide by the total number of variables. 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.

It is usually too costly or time-consuming to gather data from the entire population of interest, so data collection is limited to samples instead.

Inferential statistics utilise your sample to generate plausible assumptions about the bigger population, whereas descriptive statistics can only summarize the features of a sample.

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 has remained not-out in the matches.
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.

Difference Between Probability and Statistics: Probability vs Statistics

While probability and statistics are closely related fields, they serve different purposes and play distinct roles in analyzing and interpreting data. Probability focuses on predicting future outcomes based on theoretical models, while statistics is about analyzing and making sense of past data. Below is a detailed comparison between these two fields, highlighting their key differences and applications.

Aspect	Probability	Statistics
Definition	The study of the likelihood or chance of events happening.	The science of collecting, analyzing, and interpreting data.
Focus	Predicting the future outcomes based on known conditions or models.	Describing and summarizing past data to understand patterns.
Objective	To estimate how likely an event is to occur.	To make sense of data, identify trends, and make decisions.
Usage	Used before an experiment or event to predict outcomes.	Used after data is collected to analyze and summarize findings.
Application	Used in games, insurance, risk assessment, and AI modeling.	Applied in business, research, economics, and decision-making.
Key Question	“What is the chance that this event will happen?”	“What does this data tell us about the world or a particular event?”
Tools Used	Probability distributions, Bayes’ theorem, random variables.	Mean, median, standard deviation, regression, hypothesis testing.
Example	Predicting the likelihood of rolling a 6 on a die.	Analyzing a survey to determine average customer satisfaction.

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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FAQs

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.