Difference Between Probability and Statistics

Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events. The combination of probability and statistics helps you to improve your forecasting abilities and gain a deeper understanding of a particular situation. This article will discuss how they differ and how they can be combined to enhance your ability to make decisions.

 

Probability is a theoretical branch of mathematics which studies the consequences of mathematical definitions. In contrast, Statistics is an applied branch of mathematics which analyses the frequency of past events to draw conclusions and make predictions for the future. In this article, we will explore the difference between probability and statistics and how they can improve decision-making.

Table of Contents

• Difference Between Probability and Statistics: Probability vs Statistics
• What is Probability
• Probability Formula
• What is Statistics
• Types of Statistics

Difference Between Probability and Statistics: Probability vs Statistics

Parameter	Probability	Statistics
Definition	Probability is the measure of the likelihood that an event will occur.	Statistics is the study of collecting, analyzing, interpreting, presenting, and organizing data.
Nature	Theoretical: It deals with predicting the likelihood of future events based on a known set of possibilities.	Applied: It focuses on drawing conclusions from data that has already been collected.
Approach	Predictive: It calculates the chances of a future event occurring.	Descriptive and Inferential: It describes and analyzes past data to make inferences about future events.
Focus	Focuses on the likelihood of one or more outcomes in a defined set of outcomes.	Focuses on patterns, trends, and inferences made through the analysis of data sets.
Usage	Used to predict the likelihood of various outcomes in situations involving random variables.	Used to make sense of and interpret data and to make decisions based on data analysis.
Methods	Based on probability theory, including probability distributions and models.	Includes descriptive statistics (mean, median, mode) and inferential statistics (regression, hypothesis testing).
Applications	Common in games of chance, risk assessment, insurance, and finance.	Broadly used in fields like economics, social sciences, biology, environmental science, and market research.
Outcome	Provides a theoretical probability value based on mathematical calculations.	Provides practical insights and conclusions derived from real-world data.
Data Requirement	Does not require actual data for calculations; it works on theoretical models.	Requires real data for analysis and interpretation.

What is Probability?

Probability measures how likely something will happen, with calculations based on data collected from past events. It is expressed as a number between 0 and 1, where 0 indicates that the event cannot happen and 1 indicates that it will certainly occur.

In simple terms, the Probability is how strongly you believe an event will happen. 

For example, When you toss a coin, you will either get HEAD or TAIL. Then, the probability of getting a HEAD is 0.5, i.e., there's a 50% chance that the HEAD will come up.

Note: Probability is the foundational discipline for statistics, hypothesis testing, machine learning, and artificial intelligence.  

Probability Formula

Mathematically, the probability of any event (E) is defined as a ratio of favourable outcomes to the number of possible outcomes.

i.e., 

P(E) = Number of Favourable Outcome / Number of Possible Outcome 

0 <= P(E) <= 1

 

Must Check: Probability Formulas

Must Check: Difference Between Parameters and Statistics

 

Now, let's take an example to get a better understanding of the above formula.

Question: What is the probability of getting any specific number while rolling a dice?

Answer:

If you roll a dice, total possible outcomes are: {1, 2, 3, 4, 5, 6} 

=> P(Getting a specific Number) = P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = Number of Favorable Outcome / Total Number of Possile Outcomes = 1/6.

Therefore, the probability of getting any specific number is 1/6.

 

Question: If you toss a fair coin, what is the probability of getting exactly 50 heads?

Answer:

If you toss a coin, the probability of getting head = probability of getting tail = 1/2

Therefore, the probability of getting exactly 50 heads in 100 tosses is:

P(50 heads in 100 tosses) =  ¹⁰⁰C₅₀ * (0.5)⁵⁰ * (1 - 0.5)⁵⁰ = 0.07958 = 8% (approx).

Here, we have used the formula of Binomial Distribution.

Must Check: Top 10 Probability Interview Questions

 

What is Statistics?

Statistics is the branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It is used to make inferences about the population based on samples and to test hypotheses about the relation between variables. It also helps to make the informed decision based on data analysis.

The process of Statistics involves four key steps: Collecting Data, Organizing Data, Analyzing the Collected Data, and Interpreting Results. Before collecting any data, it's essential to define the objective or question you want to answer.

 Must Read: 11 Best Statistics Books

Types of Statistics

Statistics is broadly classified into Descriptive Statistics and Inferential Statistics.

Descriptive Statistics

It is used to summarize and describe data. It calculates the measure of central tendency (mean, median, and mode) and the measure of dispersion (variance, standard deviation, range, interquartile range).

 

Inferential Statistics

It is used to draw conclusions about population based on samples.  It uses probability theory to calculate the likelihood that certain result is due to chance.

Inferential Statistics is mainly used to test hypotheses, estimate population parameters, and make predictions.

Must Check: Statistics Interview Question for Data Science

Conclusion

Probability and Statistics are important for making informed decisions. Probability provides information about the likelihood of an event, whereas statistics helps to draw conclusions from past data to inform our decisions. Understanding of both helps in the decision-making process.