Examples of descriptive statistics in the following topics:

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

 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.
 Several descriptive statistics are often used at one time to give a full picture of the data.
 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.

 Descriptive statistics can be manipulated in many ways that can be misleading, including the changing of scale and statistical bias.
 Descriptive statistics can be manipulated in many ways that can be misleading.
 Bias is another common distortion in the field of descriptive statistics.
 Descriptive statistics is a powerful form of research because it collects and summarizes vast amounts of data and information in a manageable and organized manner.
 To illustrate you can use descriptive statistics to calculate a raw GPA score, but a raw GPA does not reflect:

 Statistical models can also be used to draw statistical inferences about the process or population under study—a practice called inferential statistics.
 Descriptive statistics and analysis of the new data tend to provide more information as to the truth of the proposition.
 This data can then be subjected to statistical analysis, serving two related purposes: description and inference.
 Descriptive statistics summarize the population data by describing what was observed in the sample numerically or graphically.
 In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible.

 A statistical model is a set of assumptions concerning the generation of the observed data and similar data.
 A statistical model is a set of assumptions concerning the generation of the observed data and similar data.
 Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference.
 Descriptive statistics are typically used as a preliminary step before more formal inferences are drawn.

 The shape of a histogram can assist with identifying other descriptive statistics, such as which measure of central tendency is appropriate to use.
 The shape of the distribution can assist with identifying other descriptive statistics, such as which measure of central tendency is appropriate to use.

 The standard error is the standard deviation of the sampling distribution of a statistic.
 However, the mean and standard deviation are descriptive statistics, whereas the mean and standard error describes bounds on a random sampling process.
 Despite the small difference in equations for the standard deviation and the standard error, this small difference changes the meaning of what is being reported from a description of the variation in measurements to a probabilistic statement about how the number of samples will provide a better bound on estimates of the population mean, in light of the central limit theorem.

 Quantitative techniques are the set of statistical procedures that yield numeric or tabular output.
 There are also many statistical tools generally referred to as graphical techniques which include:
 Below are brief descriptions of some of the most common plots:
 Histogram: In statistics, a histogram is a graphical representation of the distribution of data.
 Box plot: In descriptive statistics, a boxplot, also known as a boxandwhisker diagram, is a convenient way of graphically depicting groups of numerical data through their fivenumber summaries (the smallest observation, lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation).

 As one would expect, statistics is largely grounded in mathematics, and the study of statistics has lent itself to many major concepts in mathematics, such as:
 It includes descriptive statistics (the study of methods and tools for collecting data, and mathematical models to describe and interpret data) and inferential statistics (the systems and techniques for making probabilitybased decisions and accurate predictions based on incomplete data).
 Statistics itself also provides tools for predicting and forecasting the use of data and statistical models.
 Statistical methods date back at least to the 5th century BC.
 In this book, AlKindi provides a detailed description of how to use statistics and frequency analysis to decipher encrypted messages.

 NOTE : This example is used again in the Descriptive Statistics (Section 2.1) chapter, where the method used to compute the intervals will be explained.