[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-266541-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-266541-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","ap-statistics-exam-reference-information-formulas-and-tables","AP Statistics - Exam Reference Information - Formulas and Tables","","AP Statistics exam reference information compiling essential formulas and statistical tools for descriptive statistics, probability and distributions, sampling distributions, and inferential methods. Provides key expressions for expected value, variance, standard deviation, binomial and geometric probabilities, confidence intervals, chi-square statistics, sampling distributions for proportions and means, and regression sampling distributions with standard error guidance. Includes standard normal probability table entries and related notes for calculating z-based cumulative probabilities.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/ap-statistics-exam-reference-information-formulas-and-tables/266541/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/ap-statistics-exam-reference-information-formulas-and-tables/266541.png","ImageObject",300,407,{"name":42,"@type":43},"Asher","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What topics are covered in the AP Statistics formula tables and reference information?","Question",{"text":63,"@type":64},"It covers descriptive statistics, probability and distributions, sampling distributions, confidence intervals, chi-square statistics, and sampling distributions for proportions, means, and simple linear regression.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are confidence intervals expressed in the reference?",{"text":68,"@type":64},"A confidence interval is given as statistic ± (critical value)(standard error of statistic).",{"name":70,"@type":61,"acceptedAnswer":71},"What is included in the tables section for AP Statistics?",{"text":72,"@type":64},"The tables include Standard Normal Probabilities (Table A), listing cumulative probabilities below given z-scores.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},266541,1789408820,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145},687197207639,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","AP® Statistics  \n2026 EXAM REFERENCE INFORMATION  \nName:    \nNOTE: You may use any blank space in this booklet for scratch work during the exam. Proctors should collect this reference information at the conclusion of the exam.  \nFormulas for AP Statistics  \n\n| I. Descriptive Statistics |  |  |  |\n| --- | --- | --- | --- |\n| x 􀀠 ~~ ~~1n 􀂦xi 􀀠 ~~ ~~xi~~ ~~\u003Cbr>ˆy 􀀠 a 􀀎 bx\u003Cbr>r 􀀠 ~~ ~~n~~ ~~~~ ~~1 􀂦 􀂩􀂧􀂨 xi~~ ~~~~ ~~x~~  ~~ 􀂷􀂹􀂸 􀂧􀂩􀂨 yis~~ ~~y~~  ~~ 􀂷􀂹􀂸 | sx 􀀠 n~~ ~~~~ ~~1 􀂦􀀋xi 􀀐 x~~ ~~ 􀀌2 􀀠 y 􀀠 a 􀀎 bx\u003Cbr>b 􀀠 r  sy \u003Cbr>s\u003Cbr>x | |  |\n| II. Probability and Distributions\u003Cbr>P 􀀋 A􀂉 B 􀀌 􀀠 P 􀀋 A􀀌 􀀎 P 􀀋 B 􀀌􀀐 P 􀀋 A􀂈 B 􀀌 P (A | B) 􀀠 ~~ ~~P~~ ~~(AP(􀂈B)B) |  |  |  |\n| Probability Distribution | Mean |  | Standard Deviation |\n| Discrete random variable, X | μX = E ( X ) = 􀂦xi ⋅P (xi ) |  | \u003Cbr>2\u003Cbr>σX = 􀂦 (xi − μX ) ⋅P (xi ) |\n| If X has a binomial distribution with parameters nand p, then:\u003Cbr>P 􀀋 X 􀀠 x 􀀌 􀀠 􀂧􀂨 n 􀂷􀂸 px􀀋 1􀀐 p 􀀌n􀀐x\u003Cbr>􀂩 x 􀂹 where x 􀀠 0, 1, 2, 3, 􀀡 , n | 􀁐X 􀀠 np |  | 􀁖X 􀀠  np 􀀋 1 􀀐 p 􀀌 |\n| If X has a geometric distribution with parameter p , then:\u003Cbr>P 􀀋 X 􀀠 x 􀀌 􀀠 􀀋 1 􀀐 p 􀀌x􀀐1 p where x 􀀠 1, 2, 3, 􀀡 | 􀁐X 􀀠  1 p |  | 􀁖 􀀠 X\u003Cbr>~~ ~~ 1 􀀐 p\u003Cbr>p\u003Cbr>|\n\nIII. Sampling Distributions and Inferential Statistics  \n\n| Standardized test statistic: stanstatdardistic~~ ~~−errorpaorfamtheetsertatistic |\n| --- |\n| Confidence interval: statistic ± ( critical value )( standard error of statistic ) |\n\n\n| Chi-square statistic: | χ2 = 􀂦 ~~ ~~(~~ ~~observeed~~ ~~−expxpectedected~~ ~~)2 |\n| --- | --- |\n\nAP Statistics 1  \n© 2025 College Board  \nIII. Sampling Distributions and Inferential Statistics (continued)  \nSampling distributions for proportions:  \n\n| Random Variable | Parameters of Sampling Distribution | Standard Error* of Sample Statistic |\n| --- | --- | --- |\n|  |  |  |\n| For one population:ˆp | 􀁐ˆp 􀀠 p\u003Cbr>􀀋 􀀌\u003Cbr>\u003Cbr>􀁖ˆp\u003Cbr>p\u003Cbr>􀀠\u003Cbr>1 􀀐 p\u003Cbr>n | 􀀋 􀀌\u003Cbr>\u003Cbr>ˆ ˆ\u003Cbr>sˆp\u003Cbr>p\u003Cbr>􀀠\u003Cbr>1 􀀐 p\u003Cbr>n |\n| For two populations:ˆp1 − ˆp2 | 􀁐ˆp1 􀀐 ˆp2 􀀠 p1 􀀐 p2\u003Cbr>􀁖 ˆp1 􀀐 ˆp2\u003Cbr>􀀠\u003Cbr>| sˆp1 􀀐 ˆp2\u003Cbr>􀀠\u003Cbr>\u003Cbr>When p1 􀀠 p2 is assumed:\u003Cbr>( )\u003Cbr>\u003Cbr>sˆp1 − ˆp2 = ˆpc 1 − ˆpc\u003Cbr>􀂧􀂨􀂩\u003Cbr>1 1 􀂷+ 􀂸 n1 n2 􀂹\u003Cbr>where\u003Cbr>ˆpc 􀀠  X1 􀀎 X2  n 􀀎 n\u003Cbr>1 2 |\n\nSampling distributions for means:  \n\n| Random Variable | Parameters of Sampling Distribution |  |  | Standard Error* of Sample Statistic |  |\n| --- | --- | --- | --- | --- | --- |\n| For one population:\u003Cbr>X | 􀁐X 􀀠 􀁐 | 􀁖 ~~ ~~ 􀀠 X |  􀁖 \u003Cbr>n\u003Cbr>| \u003Cbr>ss 􀀠\u003Cbr>X\u003Cbr>n |  |\n| For two populations: X1 􀀐 X2 | 􀁐X1 􀀐 X2 􀀠 􀁐1 􀀐 􀁐2 | 􀁖 2 􀁖 2 1 2\u003Cbr>􀁖X1 􀀐 X2\u003Cbr>􀀠\u003Cbr>~~ ~~ 􀀎\u003Cbr>n1\u003Cbr>n2\u003Cbr>|  | s ~~ ~~ ~~ ~~ 􀀠 X 􀀐 X\u003Cbr>1 2 | |\n\nSampling distributions for simple linear regression:  \n\n| Random Variable | Parameters of Sampling Distribution |  |  | Standard Error* of Sample Statistic |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| For slope:\u003Cbr>b | 􀁐b 􀀠 􀁅 | \u003Cbr>􀁖\u003Cbr>􀁖b 􀀠 ,􀁖 n\u003Cbr>x |  | sb | 􀀠 | s |  |\n|  |  |  |  |  |  | sx | |\n|  |  | where 􀁖x 􀀠 | | where\u003Cbr>􀀋 􀀌\u003Cbr>\u003Cbr>s 􀀠\u003Cbr>􀂦\u003Cbr>􀀇 2 yi 􀀐 yi\u003Cbr>n􀀐 2\u003Cbr>and\u003Cbr>􀀋 ~~ ~~ 􀀌\u003Cbr>\u003Cbr>sx\u003Cbr>􀀠 􀂦 2\u003Cbr>x 􀀐 xi\u003Cbr>n􀀐1 |  |  |  |\n\n*Standard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If the standard deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standard error.  \nAP Statistics 2  \n© 2025 College Board  \nTables for AP Statistics  \n\n| \u003Cbr>Table entry for zis the probability lying below z.\u003Cbr>Table A Standard Normal Probabilities |\n| --- |\n| z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 |\n| −3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 |\n| −3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 |\n| −3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 |\n| −3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 |\n| −3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 |\n| −2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 |\n| −2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 ","cbCaikG9e5V2vmbm","https://ap.wps.com/l/cbCaikG9e5V2vmbm","pdf",3011914,11,"English","# Formulas for AP Statistics\n## I. Descriptive Statistics\n## II. Probability and Distributions\n## III. Sampling Distributions and Inferential Statistics\n# Tables for AP Statistics\n## Standard Normal Probabilities (Table A)","[{\"question\":\"What topics are covered in the AP Statistics formula tables and reference information?\",\"answer\":\"It covers descriptive statistics, probability and distributions, sampling distributions, confidence intervals, chi-square statistics, and sampling distributions for proportions, means, and simple linear regression.\"},{\"question\":\"How are confidence intervals expressed in the reference?\",\"answer\":\"A confidence interval is given as statistic ± (critical value)(standard error of statistic).\"},{\"question\":\"What is included in the tables section for AP Statistics?\",\"answer\":\"The tables include Standard Normal Probabilities (Table A), listing cumulative probabilities below given z-scores.\"}]","AP Statistics - Exam Reference Information - Formulas and Tables | PDF",28]