Sampling and Data
Statistics begins with data and how it is gathered. This chapter defines the key terms of population, sample, parameter, and statistic, explains common sampling methods and why sampling well matters, and introduces frequency tables and levels of measurement used to organise data before any analysis begins.
Key Terms: Population and Sample
Statistics is the study of how to collect, organise, analyse, and interpret data. A population is the entire group being studied, while a sample is the smaller part of it actually observed, since measuring a whole population is rarely practical. A number that describes a population is called a parameter, and a number that describes a sample is called a statistic. Because samples stand in for populations, a statistic is used to estimate the parameter it corresponds to.
Sampling Methods
How a sample is chosen decides how well it represents the population. In simple random sampling every member has an equal chance of selection, while stratified sampling divides the population into groups and draws from each. Cluster sampling selects whole groups at random, and systematic sampling takes every nth member from a list. Convenience sampling uses whoever is easiest to reach, but it risks bias because the sample may not reflect the wider population.
Frequency Tables and Levels of Measurement
A frequency table records how often each value or class appears, and relative frequency expresses that count as a proportion of the total. Data is also classified by its level of measurement: nominal data names categories, ordinal data can be ordered but its gaps are not meaningful, interval data has meaningful gaps but no true zero, and ratio data has a true zero so ratios make sense. The level of measurement guides which calculations are appropriate.