Understanding Statistics

Statistics is the branch of mathematics dealing with collection, analysis, interpretation, presentation, and organisation of data.
An important aspect is descriptive statistics, which summarise and organise data sets intuitively. Concepts include mean, median, mode, range, and standard deviation.
Inferential statistics make predictions or inferences about a population based on a sample of data. Key areas involve hypothesis testing, regression analysis, and correlation.

Data Types

Primary data is collected first-hand for a specific research purpose, while secondary data is already existing data used for a new research purpose.
Qualitative data provides insightful information but cannot be measured numerically, such as opinions or descriptions.
Quantitative data can be counted, measured, and expressed using numbers. Subtypes include discrete data (countable values) and continuous data (measurable quantities).

The mean is the sum of the data divided by the number of data points. Typically, it’s the first go-to measure of central tendency.
The median is the middle value when arranging data in ascending order. It effectively splits the data set into two halves.
The mode is the value that appears most frequently in a data set.

The range is the difference between the highest and the lowest values in a dataset.
Variance shows how individual data points differ from the mean. The square root of variance is the standard deviation, a widely used measure of variability or diversity.

Correlation measures the relationship between two variables, i.e., how they change together. It’s quantified by the correlation coefficient, which ranges from -1 to +1.
Regression analysis predicts the relationship between two or more variables.

Probability is a measure of how likely an event is to occur out of the number of possible outcomes.
Key concepts include independent events, dependent events, mutually exclusive events and exhaustive events.

This is a statistical method that uses sample data to evaluate two mutually exclusive statements about a population and makes a decision about whether to reject or fail to reject the null hypothesis.

Techniques include random sampling, systematic sampling, stratified sampling, cluster sampling, convenience sampling, etc.
Proper sampling methods ensure a more accurate representation of the population and help avoid bias.