Statistics Fundamentals

Types of Data

• Qualitative data: descriptive, categorical, and non-numerical (e.g., gender, occupation)
• Quantitative data: numerical, measurable, and can be compared (e.g., height, temperature)

Probability

• Experiment: an action or situation that can produce a set of outcomes
• Sample space: the set of all possible outcomes of an experiment
• Event: a set of one or more outcomes of an experiment
• Probability: a number between 0 and 1 that measures the likelihood of an event occurring
  • Theoretical probability: calculated using the number of favorable outcomes and total possible outcomes
  • Experimental probability: estimated based on repeated trials

Rules of Probability

• Complement rule: P(A') = 1 - P(A), where A' is the complement of event A
• Addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A and B are events
• Multiplication rule: P(A ∩ B) = P(A) × P(B), where A and B are independent events

Statistical Measures

• Mean: the average value of a dataset, sensitive to outliers
• Median: the middle value of a dataset, resistant to outliers
• Mode: the most frequent value in a dataset
• Range: the difference between the largest and smallest values in a dataset
• Variance: the average of the squared differences from the mean
• Standard deviation: the square root of the variance

Data Visualization

• Histograms: display the distribution of continuous data
• Bar graphs: compare categorical data across different groups
• Scatter plots: show the relationship between two continuous variables
• Box plots: display the distribution of continuous data and outliers

Statistical Inference

• Hypothesis testing: a procedure to test a claim about a population based on a sample
  • Null hypothesis: a statement of no effect or difference
  • Alternative hypothesis: a statement of an effect or difference
• Confidence intervals: a range of values within which a population parameter is likely to lie

Correlation and Causation

• Correlation: a statistical relationship between two variables
• Causation: a cause-and-effect relationship between two variables
• Correlation does not imply causation: a common pitfall in statistical analysis