Examples of inferential statistics in the following topics:

 The mathematical procedure in which we make intelligent guesses about a population based on a sample is called inferential statistics.
 More substantially, the terms statistical inference, statistical induction, and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from data sets arising from systems affected by random variation, such as observational errors, random sampling, or random experimentation.
 The mathematical procedures whereby we convert information about the sample into intelligent guesses about the population fall under the rubric of inferential statistics.
 Inferential statistics are based on the assumption that sampling is random.
 Discuss how inferential statistics allows us to draw conclusions about a population from a random sample and corresponding tests of significance.

 Descriptive statistics and inferential statistics are both important components of statistics when learning about a population.
 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.
 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.

 Statistics also provides tools for prediction and forecasting.
 Statistical models can also be used to draw statistical inferences about the process or population under study—a practice called inferential statistics.
 Inferential statistics uses patterns in the sample data to draw inferences about the population represented, accounting for randomness.
 Probability is used in "mathematical statistics" (alternatively, "statistical theory") to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.
 In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible.

 The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
 A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter.
 The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size n.
 It may be considered as the distribution of the statistic for all possible samples from the same population of a given size.
 The sampling distribution depends on: the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.

 This can be valuable both for making patterns in the data more interpretable and for helping to meet the assumptions of inferential statistics.

 A significance test for Pearson's r is described in the section inferential statistics for b and r.

 Recall that inferential statistics concern generalizing from a sample to a population.
 A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter.
 It is important to keep in mind that every statistic, not just the mean, has a sampling distribution.
 As we stated in the beginning of this chapter, sampling distributions are important for inferential statistics.
 Keep in mind that all statistics have sampling distributions, not just the mean.

 What would be the roles of descriptive and inferential statistics in the analysis of these data?

 This can be valuable both for making the data more interpretable and for helping to meet the assumptions of inferential statistics.

 Descriptive statistics are numbers that are used to summarize and describe data.
 Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed.
 Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section.
 You probably know that descriptive statistics are central to the world of sports.
 There are many descriptive statistics that we can compute from the data in the table.