Descriptive or Inferential Statistics?
Descriptive statistics and inferential statistics are both important components of statistics when learning about a population.
Learning Objective

Contrast descriptive and inferential statistics
Key Points
 Descriptive statistics are distinguished from inferential statistics in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
 Descriptive statistics provides simple summaries about the sample. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.
 Statistical inference makes propositions about populations, using data drawn from the population of interest via some form of random sampling. This involves hypothesis testing using a variety of statistical tests.
Terms

descriptive statistics
A branch of mathematics dealing with summarization and description of collections of data sets, including the concepts of arithmetic mean, median, and mode.

inferential statistics
A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.
Full Text
Descriptive Statistics vs. Inferential Statistics
Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data, or the quantitative description itself. Descriptive statistics are distinguished from inferential statistics in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, are not developed on the basis of probability theory. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example, in a paper reporting on a study involving human subjects, there typically appears a table giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment or exposure group), and demographic or clinical characteristics such as the average age and the proportion of subjects of each sex.
Descriptive Statistics
Descriptive statistics provides simple summaries about the sample and about the observations that have been made. Such summaries may be either quantitative, i.e. summary statistics, or visual, i.e. simpletounderstand graphs. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.
For example, the shooting percentage in basketball is a descriptive statistic that summarizes the performance of a player or a team. This number is the number of shots made divided by the number of shots taken. For example, a player who shoots 33% is making approximately one shot in every three. The percentage summarizes or describes multiple discrete events. Consider also the grade point average. This single number describes the general performance of a student across the range of their course experiences.
The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of statistics appeared. More recently, a collection of summary techniques has been formulated under the heading of exploratory data analysis: an example of such a technique is the box plot .
Box Plot
The box plot is a graphical depiction of descriptive statistics.
In the business world, descriptive statistics provide a useful summary of security returns when researchers perform empirical and analytical analysis, as they give a historical account of return behavior.
Inferential Statistics
For the most part, statistical inference makes propositions about populations, using data drawn from the population of interest via some form of random sampling. More generally, data about a random process is obtained from its observed behavior during a finite period of time. Given a parameter or hypothesis about which one wishes to make inference, statistical inference most often uses a statistical model of the random process that is supposed to generate the data and a particular realization of the random process.
The conclusion of a statistical inference is a statistical proposition. Some common forms of statistical proposition are:
 an estimate; i.e., a particular value that best approximates some parameter of interest
 a confidence interval (or set estimate); i.e., an interval constructed using a data set drawn from a population so that, under repeated sampling of such data sets, such intervals would contain the true parameter value with the probability at the stated confidence level
 a credible interval; i.e., a set of values containing, for example, 95% of posterior belief
 rejection of a hypothesis
 clustering or classification of data points into groups
Key Term Reference
 average
 Appears in these related concepts: Mean: The Average, Average Value of a Function, and Averages
 box plot
 Appears in these related concepts: Statistical Graphics, Using a Statistical Calculator, and Introduction to data solutions
 confidence interval
 Appears in these related concepts: Interpreting a Confidence Interval, Confidence Interval for a Population Mean, Standard Deviation Known, and Hypothesis Tests or Confidence Intervals?
 confidence level
 Appears in these related concepts: Level of Confidence, Lab 1: Confidence Interval (Home Costs), and Homework
 datum
 Appears in these related concepts: Change of Scale, Controlling for a Variable, and Type I and II Errors
 empirical
 Appears in these related concepts: Sociology and Science, Other Topics in M&A, and Policy Evaluation
 finite
 Appears in these related concepts: The Sample Average, Introduction to Sequences, and Summing Terms in an Arithmetic Sequence
 graph
 Appears in these related concepts: Graphical Representations of Functions, Graphing Equations, and Graphs of Equations as Graphs of Solutions
 level
 Appears in these related concepts: Factorial Experiments: Two Factors, Statistical Controls, and Randomized Design: SingleFactor
 mean
 Appears in these related concepts: Mean, Variance, and Standard Deviation of the Binomial Distribution, The Mean Value Theorem, Rolle's Theorem, and Monotonicity, and Understanding Statistics
 plot
 Appears in these related concepts: Graphs for Quantitative Data, Plotting Points on a Graph, and Introduction to Bivariate Data
 population
 Appears in these related concepts: The Functionalist Perspective on Deviance, Quorum Sensing, and Organismal Ecology and Population Ecology
 probability
 Appears in these related concepts: Theoretical Probability, Rules of Probability for Mendelian Inheritance, and The Addition Rule
 probability theory
 Appears in these related concepts: Applications of Statistics, Complementary Events, and Independence
 quantitative
 Appears in these related concepts: Preparing the Research Report, Overview of the IMRAD Model, and Math Review
 random sampling
 Appears in these related concepts: How Well Do Probability Methods Work?, Genetic Drift, and Chance Error and Bias
 range
 Appears in these related concepts: The Derivative as a Function, Visualizing Domain and Range, and Introduction to Domain and Range
 sample
 Appears in these related concepts: Identifying Product Benefits, Surveys, and Basic Inferential Statistics
 sampling
 Appears in these related concepts: Collecting and Measuring Data, Continuous Sampling Distributions, and Confidence Interval, Single Population Mean, Standard Deviation Unknown, Student'st
 statistics
 Appears in these related concepts: Communicating Statistics, Population Demography, and What Is Statistics?
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