[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-571681-105":3,"detail-sidebar-cat-1-en-105":81,"doc-detail-571681-en":127},{"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","13-statistics-packet","13-Statistics Packet","","Statistics formula sheet organized into chapters covering class width, midpoint, and key mean measures including sample, population, and weighted means. Includes frequency-table mean, midrange, range, standard deviation, variance, and the empirical rule for normal distributions. Provides formulas for coefficient of variation, z-scores, interquartile range and modified box-plot outlier limits, plus probability rules, permutations, combinations, discrete distributions (binomial, Poisson), normal distribution scoring, confidence intervals, hypothesis testing, and regression/correlation statistics.",{"@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/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/presentations/","Presentations",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/13-statistics-packet/571681/",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/13-statistics-packet/571681.png","ImageObject",442,249,{"name":42,"@type":43},"I feel Different","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-21","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How are class width and class midpoint calculated in Chapter 2?","Question",{"text":63,"@type":64},"Class width is based on the difference between the highest and lowest class limits (then rounded to the next integer as indicated). Class midpoint equals the upper limit plus the lower limit.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What formulas define confidence intervals for proportions and means in Chapter 7?",{"text":68,"@type":64},"For proportions, the interval is given as np and nq conditions with error E defined using zα/2 and p(1−p) over n. For means, when σ is known the interval is x ± E with E = zα/2 times σ over √n, and when σ is unknown it uses tα/2 with s over √n and d.f. = n − 1.",{"name":70,"@type":61,"acceptedAnswer":71},"Which probability rules and distribution formulas are included across Chapters 4 and 5?",{"text":72,"@type":64},"Chapter 4 provides complement, multiplication for independent events, general multiplication, addition for mutually exclusive events, and general addition, plus permutation and combination rules. Chapter 5 gives mean and standard deviation for discrete distributions, then binomial distribution parameters and probability P(r), and Poisson distribution probability P(r) with σ = µ.","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},571681,1792022899,{"code":4,"msg":82,"data":83},"success",[84,88,93,98,103,108,113,118,123],{"id":85,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":86,"slug":87},11,90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social Media",50,"social-media",{"id":109,"doc_module":22,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},17,"Forms",40,"forms",{"id":114,"doc_module":22,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},18,"Letters",30,"letters",{"id":119,"doc_module":22,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},21,"Paper Templates",5,"papers-templates",{"id":124,"doc_module":22,"doc_module_name":25,"category_name":125,"show_sort_weight":4,"slug":126},158,"General","general-158",{"code":4,"msg":82,"data":128},{"doc_id":79,"user_id":129,"nickname":42,"user_avatar":130,"doc_module":22,"category_id":85,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":89,"language":136,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":12,"update_tm":140,"read_time":33},962093541761,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Chapter 2  \nClass Width = highestnvuueber-lowestclasses~~ ~~value~~ ~~ (increase to next integer)  \nClass Midpoint = upper limit + lower limit  \n2  \nChapter 3  \nn = sample size N = population size f = frequency  \nΣ = sum w = weight  \nSample mean: x = ~~ ~~x  \nPopulation mean: µ = ~~ ~~x  \nWeighted mean: x = ∑•wx)  \nMean for frequency table: x = ~~ ~~∑x) Midrange =  highest value + lowest value  \n2  \nRange = Highest value-Lowest value Sample standard deviation: s = ∑(xn~~ ~~−x1)2~~ ~~  \nPopulation standard deviation: σ = ∑(x − µ)2   \n N  \nSample variance: s 2  \nPopulation variance: σ 2  \nChapter 3  \nLimits for Unusual Data Below : µ -2σ  \nAbove: µ + 2σ  \nEmpirical Rule  \nAbout 68%: µ -σ to µ + σ About 95%: µ-2σ to µ + 2σ About 99.7%: µ-3σ to µ + 3σ  \nSample coefficient of variation: CV = ~~  ~~s 􀀼 100%  \nx  \nPopulation coefficient of variation: CV = ~~ ~~σµ 􀀼 100%  \nSample standard deviation for frequency table:  \n n [ ∑( f • x2 ) ] −[ ∑( f • x) ] 2   \ns =  n (n −1)  \nSample z-score: z = ~~ ~~x~~ ~~−s~~ ~~x  \nPopulation z-score: z = ~~ ~~x~~ ~~~~ ~~µ  \nInterquartile Range: (IQR) = Q3 − Q1  \nModified Box Plot Outliers lower limit: Q1 -1.5 (IQR)  \nupper limit: Q3 + 1.5 (IQR)  \nChapter 4  \nProbability of the complement of event AP (not A) = 1 - P (A)  \nMultiplication rule for independent events P (A and B) = P (A) • P (B)  \nGeneral multiplication rules  \nP (A and B) = P (A) • P (B, given A)  \nP (A and B) = P (A) • P (A, given B)  \nAddition rule for mutually exclusive events P (A or B) = P (A) + P(B)  \nGeneral addition rule  \nP (A or B) = P (A) + P (B) − P(A and B)  \nPermutation rule: n Pr = ~~ ~~(n~~ ~~!r)!  \nCombination rule: C =  n!   \nn r r !(n − r)!  \nPermutation and Combination on TI 83/84  \nn  Math   PRB   nPr   enter  r  \nn  Math   PRB   nCr   enter  r  \nNote: textbooks and formula sheets interchange “r” and “x”for number of successes  \nChapter 5  \nDiscrete Probability Distributions:  \nMean of a discrete probability distribution:  \nµ = ∑[x • P(x)]  \nStandard deviation of a probability distribution:  \nσ = ∑[x2 • P(x)] − µ 2  \nBinomial Distributions  \nr = number of successes (or x) p = probability of success q = probability of failure  \nq = 1−p p + q = 1  \nBinomial probability distribution P (r) = n Cr pr q n−r  \nMean: µ = np  \nStandard deviation: σ = npq  \nPoisson Distributions  \nr = number of successes (or x)  \nµ = mean number of successes  \n(over a given interval) Poisson probability distribution  \nP (r) = ~~ ~~e~~ ~~−~~ ~~µr~~ ~~!µ~~ ~~r~~ ~~e ≈ 2.71828  \nµ = mean (over some interval)  \nσ = µ  \n2  \nσ = µ  \nChapter 6  \nNormal Distributions  \nRaw score: x = zσ + µ  \nx − µ  \nStandard score: z =  \nσ  \nMean of x distribution: µx = µ  \nStandard deviation of x distribtuion: σx =(standard error)  \nStandard score for x : z = ~~ ~~xσ/−~~ ~~µn~~  ~~  \nChapter 7  \nOne Sample Confidence Interval  \nfor proportions (p) : (np > 5 and nq > 5)  − E \u003C p \u003C  + E  \nwhere E = zα /2 p (1− p)  \nn  \n= ~~ ~~rn  \nfor means ( µ) when σ is known:  \nx − E \u003C µ \u003C x + E where E = zα /2 ~~ ~~σn  \nfor means ( µ) when σ is unknown:  \nx − E \u003C µ \u003C x + E  \nwhere E = tα /2 ~~ ~~sn with d.f . = n −1  \nσ  \nn  \nChapter 7  \nConfidence Interval: Point estimate ± error Point estimate = Upper limit + Lower limit  \n2  \nError = Upper limit-Lower limit  \n2  \nSample Size for Estimating  \nmeans:  \nn = 􀂧  zα /2 σ  􀂷 2  \n􀂩􀂨 E 􀂹􀂸  \nproportions:  \nn =  􀂧􀂨􀂩 ~~ ~~zα~~ /2~~E~~ ~~􀂷􀂹􀂸 2 with preliminary estimate for pn = 0.25 􀂧􀂨􀂩 ~~ ~~zα~~ /2~~E~~ ~~􀂷􀂹􀂸 2 without preliminary estimate for p variance or standard deviation:  \n*see table 7-2 (last page of formula sheet)  \nConfidence Intervals  \nLevel of Confidence z-value ( zα /2 )  \n70%  \n75%  \n80%  \n85%  \n90%  \n95%  \n98%  \n99%  \n1.04  \n1.15  \n1.28  \n1.44  \n1.645  \n1.96  \n2.33  \n2.58  \nfor variance ( σ 2 ) : (n~~ ~~12R)s2~~ ~~ \u003C σ 2 \u003C ~~ ~~(n~~ ~~12L)s2~~  ~~with d.f . = n −1  \nChapter 8  \nOne Sample Hypothesis Testing  \nfor p (np > 5 and nq > 5) : z = ~~ ~~−q where q = 1− p; = r / n  \nfor µ ( σ known): z = ~~ ~~xσ/−µn  \nfor µ ( σ unkn","cbCaikIyO5Zk8MpE","https://ap.wps.com/l/cbCaikIyO5Zk8MpE","pdf",624862,"English","# Chapter 2\n## Class Width and Class Midpoint\n# Chapter 3\n## Mean, Midrange, Range\n## Variance, Standard Deviation, Empirical Rule\n## Coefficient of Variation and Z-Score\n## Interquartile Range and Modified Box Plot\n# Chapter 4\n## Probability Rules\n## Permutations and Combinations\n# Chapter 5\n## Discrete Probability Distributions\n## Binomial and Poisson Distributions\n# Chapter 6\n## Normal Distributions and Standard Scores\n# Chapter 7\n## One-Sample Confidence Intervals\n# Chapter 8\n## One-Sample Hypothesis Testing\n# Chapter 9\n## Two-Sample Confidence Intervals and Tests\n## Difference of Proportions and Means\n## Matched Pairs and Variances\n# Chapter 10\n## Regression and Correlation","[{\"question\":\"How are class width and class midpoint calculated in Chapter 2?\",\"answer\":\"Class width is based on the difference between the highest and lowest class limits (then rounded to the next integer as indicated). Class midpoint equals the upper limit plus the lower limit.\"},{\"question\":\"What formulas define confidence intervals for proportions and means in Chapter 7?\",\"answer\":\"For proportions, the interval is given as np and nq conditions with error E defined using zα/2 and p(1−p) over n. For means, when σ is known the interval is x ± E with E = zα/2 times σ over √n, and when σ is unknown it uses tα/2 with s over √n and d.f. = n − 1.\"},{\"question\":\"Which probability rules and distribution formulas are included across Chapters 4 and 5?\",\"answer\":\"Chapter 4 provides complement, multiplication for independent events, general multiplication, addition for mutually exclusive events, and general addition, plus permutation and combination rules. Chapter 5 gives mean and standard deviation for discrete distributions, then binomial distribution parameters and probability P(r), and Poisson distribution probability P(r) with σ = µ.\"}]","13-Statistics Packet | PDF",1791923099]