Probability and Statistics
Probability and statistics are important mathematical underpinnings. Most statistical applications are founded on probability. Key elements in probability, data presentations, and statistical variability are some essential artifacts that serve as the foundation of probability and statistics in mathematics. Statistical variability is mostly dependent on giving each sample an equal chance of being used in any study. When performing any type of research in mathematical contexts, statistical variability ensures that outliers are avoided. A key artifact used to ensure statistical variability is random sampling which requires each sample to be selected without any form of bias (Grimmett 292). Probability processes involve the prediction of outcomes and must, therefore, be based on random sampling for accurate results to be obtained. This information is also supposed to be presented in a manner that indicates the presence and use of the aforementioned characteristics. These domains are significant since they identify critical aspects of mathematics that form the basis of any form of research. It also provides information on how to deal with probable information presented in any form. All of these domains are supposed to be addressed through the various learning models and more so during secondary and collegiate studies.
Probability and Sampling
Probability and sampling define numerous features in mathematics. First, it serves as the foundation of several key mathematical attributes, including aspects related to calculus and mathematical research. Random sampling serves to provide crucial information which ensures that mathematical data is reliable and valid. In case random sampling is not used in any mathematical process, then the information provided is bound to have a higher number of outliers (Dankowski and Ziegler 3949). In addition, the information is more likely not to be reliable, especially when similar research is conducted based on a similar protocol. After conducting research, it becomes necessary to present information in some of the common methods to investigate the spread of data across all points. Data distribution and presentation methods serve to indicate whether the information provided is reliable and valid.
Random Sampling and Probability in Education
Random sampling and probability are two essential elements commonly present in secondary mathematics and in college. These two aspects form the basis of most fundamental concepts. In addition, they serve to provide basic fundamental information required in carrying out research. Mathematical research is supposed to start at a tender age and more so in secondary school. During this time, students are supposed to be taught fundamental aspects related to research, especially issues related to statistical variability and methods of presenting data. After critical elements have been learned during this process, students are supposed to solely use this information in their collegiate education, especially in conducting further research in areas in mathematics (Grimmett 291). At this stage, students are taught how to use random sampling as an effective means of carrying out mathematical tests. All of this information is critical in ensuring that mathematical research falls under the required domain.
Application of Probability and Sampling in Research
Information related to probability and random sampling has been used severally in research in investigating different variables. For example, this has been used in research projects to investigate variables in modeling based on calculus formulas. For example, in investigating the transmission rates of a disease, statistics, and random sampling will be used during the entire process.
Work Cited
Dankowski, Theresa, and Andreas Ziegler. ‘Calibrating Random Forests for Probability Estimation’. Statistics in Medicine, vol. 35, no. 22, 2016, pp. 3949–3960.
Grimmett, Geoffrey. ‘Probability on Graphs: Random Processes on Graphs and Lattices’. Contemporary Physics, vol. 53, no. 3, 2012, pp. 291–292.
