Basic Statistics in Mathematics

Summary:

This text introduces the concept of statistics and its various meanings. Statistics can refer to recorded data, characteristics of groups, and methods of data analysis, and is defined as a science dealing with data collection, presentation, analysis, and interpretation. It is concerned with understanding data structures and helps make reliable descriptions, objective statements, and evidence-based decisions.

Statistical investigation involves problem identification, data collection, presentation, analysis, and interpretation. It distinguishes between population (total collection of values) and sample (a subset of values). Descriptive statistics summarize data characteristics, while inferential statistics use sample data to infer population characteristics.

Data can be qualitative (non-numeric attributes) or quantitative (numbers representing measurements). Quantitative data can be discreet (countable values) or continuous (infinitely many values on a range). Data measurement levels include nominal (categorization), ordinal (ranking), interval (meaningful differences without true zero), and ratio (meaningful ratios with true zero).

Data collection methods include direct (interviews, registration, observation, experiments, questionnaires) and indirect (using existing data sources). Sampling techniques involve probability (random, systematic, stratified, multi-stage, cluster) and non-probability (purposive, quota, convenience) methods.

Excerpt:

Basic Statistics in Mathematics

INTRODUCTION TO STATISTICS

The term statistics has several meanings. Sometimes it is used to refer to any recorded data such as the number of enrollees, the common size of classes, the number of patients, and the average score of nurses from board examination. It is also used to denote some characteristics of a group or set of objects, such as mean, median, standard deviation and coefficient of correlation. Another meaning of statistics refers to the method or procedure of analysis of data. And universally, it is being defined as:

Statistics– a science that deals with collection, presentation, analysis, and interpretation of data.

Statistics is fundamentally concerned with the understanding of structures of data. Methods range from simple to more systematic procedures in describing and summarizing data. These methods enable us to develop a way of thinking. This helps us:

• describe or characterized persons, objects, situations and phenomena with some reliability
• make statements and comparisons in an objective manner
• make evidence-based decisions