Lotus BlogTheory - [T12]
Descriptive Statistics
Descriptive Statistics is a data analysis approach that is applied to summarize and present data in a meaningful way. It extrapolates information from a given Dataset or sample population, and computes useful and easy to understand information, as, for example, measures of central tendency (e.g. mean, median, etc.).
The Role of Probability
In Descriptive Statistics, Probability is used to understand the likelihood of a certain event falling into a specific interval of the Dataset.
The Role of Probability Distributions
Probability Distributions are often used to better visualize and present the data that are observed in the Dataset. In particular it is very useful to utilize scatterplots, histograms or probability density functions to represent the distributions of the dataset, and understand better the population which is the object of observation.
Inferential Statistics
Inferential Statistics, differently from Descriptive Statistics, and as the name suggests, is used to infer information of a theoretical population, given a subset of it. In fact it uses the data extrapolated from a smaller sample to make predictions or generalizations on the larger population.
The Role of Probability
Probability is used in Inferential Statistics, to validate, the likelihood of an event observed on the study sample, to be a valid representative for the theoretical population. For these reason, various techniques such as Hypothesis Testing or Regression Analysis are used in correlation with Probability to measure the uncertainty of our inferences.
The Role of Probability Distributions
Probability Distributions are simply essential for Inferential Statistics, and they represent the basis used in the inference process. In fact a crucial step in Inferential Statistics is the choice of the distribution used to represent the population object of the study. Choosing a certain distribution over another one can prove to be crucial in obtaining the accuracy needed to correctly perform the inference using the techniques mentioned above.
Sources
- https://en.wikipedia.org/wiki/Descriptive_statistics
- https://en.wikipedia.org/wiki/Statistical_inference
- https://www.statology.org/descriptive-inferential-statistics/
- https://statisticsbyjim.com/basics/descriptive-inferential-statistics/
- https://www.scribbr.com/frequently-asked-questions/whats-the-difference-between-descriptive-and-inferential-statistics/
- https://www.scribbr.com/statistics/descriptive-statistics/
- https://www.scribbr.com/statistics/inferential-statistics/
- https://www.cse.iitk.ac.in/users/piyush/courses/pml_fall17/material/probabilty_tutorial.pdf
- https://en.wikipedia.org/wiki/Probability_distribution