[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-42881-en":3,"doc-seo-42881-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},42881,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","An Introduction to Statistics","An Introduction to Statistics presents the foundational tools used to summarize data and reason about uncertainty. It explains descriptive versus inferential statistics, introduces central measures such as mean, median, and mode, and covers variability, position, and dispersion concepts. It also introduces common graphical displays including histograms, stem-and-leaf plots, and box-and-whisker summaries. The text progresses to probability, random variables, key distributions (binomial, Poisson, normal), and then to estimating population mean via confidence intervals and hypothesis testing.","An Introduction to Statistics  \nKeone Hon \u003C[keone.hon@gmail.com](keone.hon@gmail.com) >  \nContents  \n1 Descriptive Statistics 2  \n1.1 Descriptive vs. Inferential ...................... 2  \n1.2 Means, Medians, and Modes ..................... 2  \n1.3 Variability ............................... 4  \n1.4 Linear Transformations ....................... 5  \n1.5 Position ................................ 6  \n1.6 Dispersion Percentages ........................ 7  \n2 Graphs and Displays 9  \n2.1 Histograms .............................. 9  \n2.1.1 Introduction ......................... 9  \n2.1.2 Medians, Modes, and Means Revisited ........... 10  \n2.1.3 z-Scores and Percentile Ranks Revisited .......... 11  \n2.2 Stem and Leaf Displays ....................... 11  \n2.3 Five Number Summaries and Box and Whisker Displays ..... 12  \n3 Probability 13  \n3.1 Introduction .............................. 13  \n3.2 Random Variables .......................... 16  \n3.2.1 De􀀌nition ........................... 16  \n3.2.2 Expected Value ........................ 17  \n3.2.3 Variance and Standard Deviation .............. 17  \n3.2.4 \\Shortcuts\" for Binomial Random Variables ........ 18  \n4 Probability Distributions 19  \n4.1 Binomial Distributions ........................ 19  \n4.2 Poisson Distributions ......................... 21  \n4.2.1 De􀀌nition ........................... 21  \n4.2.2 As an Approximation to the Binomial ........... 22  \n4.3 Normal Distributions ......................... 23  \n4.3.1 De􀀌nition and Properties .................. 23  \n4.3.2 Table of Normal Curve Areas ................ 23  \n4.3.3 Working Backwards ..................... 25  \n4.3.4 As an Approximation to the Binomial ........... 26  \n5 The Population Mean 28  \n5.1 The Distribution of Sample Means ................. 28  \n5.2 Con􀀌dence Interval Estimatess ................... 29  \n5.3 Choosing a Sample Size ....................... 30  \n5.4 The Hypothesis Test ......................... 31  \n5.5 More on Errors ............................ 32  \n5.5.1 Type I Errors and Alpha-Risks ............... 32  \n5.5.2 Type II Errors and Beta-Risks ............... 34  \n5.6 Comparing Two Means ....................... 35  \n5.6.1 Con􀀌dence Interval Estimates ................ 35  \nChapter 1  \nDescriptive Statistics  \n1.1 Descriptive vs. Inferential  \nThere are two main branches of statistics: descriptive and inferential. Descriptive statistics is used to say something about a set of information that has been collected only. Inferential statistics is used to make predictions or comparisons about a larger group (a population) using information gathered about a small part of that population. Thus, inferential statistics involves generalizing beyond the data, something that descriptive statistics does not do.  \nOther distinctions are sometimes made between data types.  \n􀀏 Discrete data are whole numbers, and are usually a count of objects. (For instance, one study might count how many pets di􀀋erent families own; it wouldn't make sense to have half a gold􀀌sh, would it?)  \n􀀏 Measured data, in contrast to discrete data, are continuous, and thus may take on any real value. (For example, the amount of time a group of children spent watching TV would be measured data, since they could watch any number of hours, even though their watching habits will probably be some multiple of 30 minutes.)  \n􀀏 Numerical data are numbers.  \n􀀏 Categorical data have labels (i.e. words) . (For example, a list of the products bought by di􀀋erent families at a grocery store would be categorical data, since it would go something like fmilk, eggs, toilet paper, . . . g.)  \n1.2 Means, Medians, and Modes  \nIn everyday life, the word \\average\" is used in a variety of ways - batting averages, average life expectancies, etc. - but the meaning is similar, usually  \nthe center of a distribution. In the mathematical world, where everything must be precise, we de􀀌ne several ways of 􀀌nding the center of a set of data:  \nDe􀀌nition 1: median.  \nThe median ","cbCaimsjykpfYtSQ","https://ap.wps.com/l/cbCaimsjykpfYtSQ","pdf",372548,3,1,43,"English","en",105,"# Descriptive Statistics\n## Descriptive vs. Inferential\n## Means, Medians, and Modes\n## Variability\n## Linear Transformations\n## Position\n## Dispersion Percentages\n# Graphs and Displays\n## Histograms\n## Stem and Leaf Displays\n## Five Number Summaries and Box and Whisker Displays\n# Probability\n## Introduction\n## Random Variables\n# Probability Distributions\n## Binomial Distributions\n## Poisson Distributions\n## Normal Distributions\n# The Population Mean\n## Distribution of Sample Means\n## Confidence Interval Estimates\n## Choosing a Sample Size\n## The Hypothesis Test","[{\"question\":\"What is the difference between descriptive and inferential statistics?\",\"answer\":\"Descriptive statistics summarizes information collected from a dataset. Inferential statistics makes predictions or comparisons about a larger population using information from a smaller part of that population.\"},{\"question\":\"How are median, mode, and mean used to describe the center of data?\",\"answer\":\"The median is the middle value after ordering, and it is not affected by extreme values. The mode is the most frequent value and can be bimodal. The mean is the sum of values divided by the number of values.\"},{\"question\":\"What major topics does the book cover after probability distributions?\",\"answer\":\"After introducing probability distributions like binomial, Poisson, and normal, it moves to the population mean, including the distribution of sample means, confidence interval estimation, choosing sample size, and hypothesis testing with error types.\"}]",1783372497,108,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"an-introduction-to-statistics","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/an-introduction-to-statistics/42881/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-13","2026-07-06",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the difference between descriptive and inferential statistics?","Question",{"text":75,"@type":76},"Descriptive statistics summarizes information collected from a dataset. Inferential statistics makes predictions or comparisons about a larger population using information from a smaller part of that population.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are median, mode, and mean used to describe the center of data?",{"text":80,"@type":76},"The median is the middle value after ordering, and it is not affected by extreme values. The mode is the most frequent value and can be bimodal. The mean is the sum of values divided by the number of values.",{"name":82,"@type":73,"acceptedAnswer":83},"What major topics does the book cover after probability distributions?",{"text":84,"@type":76},"After introducing probability distributions like binomial, Poisson, and normal, it moves to the population mean, including the distribution of sample means, confidence interval estimation, choosing sample size, and hypothesis testing with error types.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]