LeI A and B be III x" lIlall ices. Show that A is equivalent to B if and only if A T is equivalent to BT.

Statistics Math 181, Spring 2016 Statistics is the science of gathering, describing, and analyzing data. Statistics are also the numerical descriptions of data. Population= all of the people/things that one is trying to learn about Sample = a group of the population from which data is collected (the Sample is a group from the Population) Population vs. Sample ● Whole group ● Part of the group ● Want to know about ● Do know about ● Characteristics = Parameters ● Characteristics = Statistics ● Parameters = fixed & unknown ● Statistics are known & can change Data= Measurements, Counts, or Observations gathered in regards to a specific variable in a population. Variable= a value/characteristic that changes among population members Census= a study in which data is obtained from every member of the population Parameter= a numerical description of a population characteristic(s) Statistic= numerical descriptions of sample characteristic(s) Branches of Statistics Descriptive Statistigather, sort, summarize, and display data. Inferential Statistiinvolves using descriptive statistics to estimate population parameters. Data Qualitative Data(QL) = categorical da(this includes descriptions/qualities) Quantitative Data(QN) = numerical data(measurements, counts, & other quantities) Quantitative da