The foundation of data science comprises statistics and probability, which aid in understanding and modeling data uncertainties and trends. Below is a summary of their functions and important data science concepts:
Statistics for Data Science
Descriptive Statistics:
These offer an overview of the key characteristics of the data. Typical examples of descriptive statistics are:
Mean, Median, Mode: Measures of central tendency that characterize the average or most prevalent value are mean, median, and mode.
Source: Probability and Statistics
Variance and Standard Deviation: Measures of data dispersion that indicate how much results deviate from the mean are called variance and standard deviation.
Percentiles and Quartiles: To comprehend data distribution and how it disperses over a range, utilize percentiles and quartiles.
Kurtosis and Skewness: Explain how the data distribution is shaped in terms of asymmetry (skewness) and the existence of extreme values or outliers (kurtosis).
Inferential Statistics:
Using a sample, inferential statistics facilitate the process of concluding the population:
Hypothesis Testing: This includes comparing groups or testing population parameter assumptions using techniques like ANOVA, chi-square testing, and t-tests.
Confidence intervals: These give an expected range of values for a population parameter with a given probability.
P-values: Assist in establishing the statistical significance of the observed data in confirming a hypothesis.
Regression Analysis:
Linear Regression: Models the connection between one or more independent variables and a dependent variable using linear regression. It aids in the prediction of ongoing results.
Logistic Regression: When doing binary classification tasks with a categorical dependent variable, logistic regression is utilized.
Source: Probability for Data Science
Probability for Data Science
Probability Theory:
The majority of machine learning algorithms are based on probability theory. It is crucial for creating prediction models as it measures the probability of occurrences.
Basic Probability Concepts: Sample spaces, conditional probability, and events are examples of basic probability concepts.
Bayes’ Theorem: Fundamental to probability, particularly in Bayesian statistics, the Bayes Theorem aids in updating beliefs in response to fresh data.
Law of Large Numbers: The Law of Large Numbers asserts that a sample’s mean approaches the population average as its size increases.
Central Limit Theorem (CLT): The Central Limit Theorem (CLT), which is essential for many inferential statistics techniques, states that as sample size rises, the distribution of the sample mean approaches a normal distribution.
Source: Probability, Statistics, Data Science and Machine Learning
Distributions:
Discrete Distributions: These comprise the distributions utilized in scenarios with discrete outcomes, such as the Poisson, geometric, and binomial distributions.
Continuous Distributions: Distributions that characterize continuous outcomes include normal, exponential, and uniform distributions.
In data science, it is essential to comprehend these distributions to build models, make deductions, and run simulations.
Markov Chains and Random Processes:
Markov Chains: Models in which the course of events that precede an event determines the future state only from the current state.
Monte Carlo Simulation: Monte Carlo simulation is a valuable tool for evaluating the effects of risk and uncertainty in prediction models. It computes findings through repeated random sampling.
Applications in Data Science
Machine learning algorithms: Probability theory is the foundation of several algorithms, including Hidden Markov Models and Naive Bayes.
A/B testing: Based on statistical evidence, this type of hypothesis testing is frequently used in data science to assess the performance of two versions (e.g., website designs, and marketing tactics).
Data-Driven Decisions: By recognizing patterns, correlations, and causal relationships, statistics help organizations deduce insights from data to inform strategic decision-making.
In data science, probability and statistics are essential for comprehending data distributions, drawing conclusions, and creating prediction models. They provide the basis for nearly every data-driven job, ranging from sophisticated machine learning algorithms to exploratory data analysis.