Intro to Elementary Statistics

Elementary statistics is the study of variables, populations, samples, and data analysis techniques. Descriptive statistics involves collecting, organizing, summarizing, and presenting data, while inferential statistics involves generalizing from samples to populations, performing estimations and hypothesis testing, determining relationships between variables, and making predictions. Variables can be qualitative or quantitative. Qualitative variables have distinct categories, while quantitative variables can be measured or counted. Discrete variables can be counted, while continuous variables can take on an infinite number of values. Nominal level of measurement classifies data into mutually exclusive categories, while ordinal level of measurement allows data to be ranked. Interval level of measurement compares data between different members of the population. Data can be collected through random sampling, systematic sampling, stratified sampling, or cluster sampling. Random sampling gives all members of the population an equal chance of being selected, while systematic sampling selects every Kth member of the population. Stratified sampling divides the population into subgroups and selects subjects randomly from each subgroup. Cluster sampling divides the population into clusters and selects one or more clusters randomly. Experimental studies involve manipulating variables to determine their influence on other variables, while observational studies observe and draw conclusions based on past observations. Measures of variation include the interquartile range, which is the difference between the first and third quartiles, and the five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum. The empirical rule is used to determine the proportion of data within certain standard deviations from the mean. Lastly, pie charts and bar charts are graphical tools used to represent data.