- Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.
- Data can be classified into two main types: qualitative (categorical) data, which describes characteristics or attributes, and quantitative (numerical) data, which represents measurements or quantities.
- Descriptive statistics involves summarizing and describing data through measures such as measures of central tendency (mean, median, mode) and measures of variability (standard deviation, range).
- Inferential statistics uses sample data to make inferences or draw conclusions about a larger population. It involves techniques such as hypothesis testing, confidence intervals, and regression analysis.
- Probability is a fundamental concept in statistics that quantifies the likelihood of an event occurring. It provides a theoretical foundation for statistical analysis and inference.
- Sampling is the process of selecting a subset of individuals or units from a population to gather data. Proper sampling techniques are crucial to obtaining representative and unbiased results.
- The normal distribution, also known as the Gaussian distribution or bell curve, is a symmetrical probability distribution frequently used in statistics. Many natural phenomena and measurements tend to follow this distribution.
- Statistical significance is a measure of the likelihood that an observed result is not due to chance. It is often determined through hypothesis testing, where the null hypothesis is tested against an alternative hypothesis.

- Regression analysis examines the relationship between a dependent variable and one or more independent variables. It is used to model and predict outcomes based on observed data.
- Correlation measures the strength and direction of the relationship between two variables. A correlation coefficient of +1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and 0 indicates no relationship.
- Probability distributions, such as the binomial, Poisson, and exponential distributions, provide mathematical models for random variables and their probabilities of occurrence.
- Experimental design involves planning and controlling experiments to maximize the validity of conclusions. It includes considerations such as randomization, replication, and control groups.
- Statistical software packages, such as R, Python (with libraries like NumPy and Pandas), and SPSS, facilitate data analysis, visualization, and statistical modeling.
- Sampling error refers to the discrepancy between sample statistics and population parameters. It is inherent in sampling and can be minimized by increasing the sample size.
- Statistical literacy and critical thinking are essential skills for interpreting and evaluating statistical information presented in various contexts, including scientific studies, surveys, and media reports.