[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-300373-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-300373-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","fe-review-statistics","FE Review - Statistics","","FE Review - Statistics covers key quantitative topics for the FE exam, including measures of central tendency and dispersion, uncertainty, and confidence intervals. It reviews core probability laws and common distributions, expected value, and regression with goodness of fit using metrics such as correlation coefficient and R2. The material also includes sampling and hypothesis testing, ANOVA and factorial design, plus foundational definitions for population, sample, parameters, statistics, variation, and probability. Worked examples illustrate sample variance, median, mode, and computing confidence intervals using Student-t and Z methods.",{"@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/fe-review-statistics/300373/",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/fe-review-statistics/300373.png","ImageObject",300,407,{"name":42,"@type":43},"Liam","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-21","2026-09-18",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What statistical topics are covered in the FE review for statistics?","Question",{"text":63,"@type":64},"The review covers central tendency and dispersion, measures of uncertainty, confidence intervals, probability laws and distributions, expected value, regression and goodness of fit, sampling and hypothesis testing, and ANOVA/factorial design.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are population, sample, parameter, and statistic defined in the document?",{"text":68,"@type":64},"Population is the full collection of measurements of interest, a sample is a subset extracted from the population, a parameter is a characteristic of the population, and a statistic is a characteristic of the sample.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you choose between Student-t and Z when computing confidence intervals for the mean?",{"text":72,"@type":64},"Use Student-t when the standard deviation is unknown, and use Z when the standard deviation (variance) is known, as shown in the worked examples.","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},300373,1789773996,{"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,"preview_page_count":4},8796095461564,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","FE Review ‐ Statistics  \nDR . GERRY KNAPP, P. E . (LOUISIANA)  \nStatistics Topics on FE  \nNumber of questions:  \n◦ Chemical: 4–6  \n◦ Civil: 2‐3?(part of math)  \n◦ Electrical: 4–6  \n◦ Environmental: 4–6  \n◦ Industrial: 10–15  \n◦ Mechanical: 4–6  \n◦ Other: 6–9  \n\n| Measures of central tendencies and dispersions (e.g., mean, mode, standard deviation), measurement uncertainty, confidence intervals. IE, ChE: control limits | All |\n| --- | --- |\n| Basic laws of probability & probability distributions (e.g., discrete, continuous, normal, binomial, empirical). EE & IE: Conditional probability; IE: permutations & combinations, sets | All |\n| Expected value (weighted average) | All |\n| Regression & goodness of fit (linear, multiple, curve fitting, correlation coefficient, R2, least squares). IE: Residual analysis | All |\n| Sampling & hypothesis testing (central limit, sampling distributions, standard error, normal, t, chi‐square, types of error, sample size, outlier testing, significance) | ChE, EE, IE, Other |\n| Analysis of Variance (ANOVA). IE: Factorial Design | Che, IE, EE |\n\nDefinitions  \nPopulation  \n◦ Collection of all measurements of interest to the statistical analysis.  \n◦ May be of infinite size.  \nSample  \n◦ Subset of data extracted from population (usually randomly)  \nParameter  \n◦ Characteristic of population  \nStatistic  \n◦ Characteristic of sample  \nVariation: changes, differences, uncertainty, randomness in a population  \nProbability: two (equivalent) perspectives:  \n◦ Percentage of a population meeting some criteria  \n◦ Chance of any one observation from the population meeting some criteria  \nMeasures of central tendencies and dispersions  \nCommon Statistics  \n\n| STATISTIC | SYMBOL | FORMULA | Population\u003Cbr>Symbol |\n| --- | --- | --- | --- |\n| Mean | ത􀜺 | ∑ 􀜺௜\u003Cbr>􀝊 | 􀁐 |\n| Median | m | Order data smallest to largest\u003Cbr>If n is odd, middle value;\u003Cbr>if n is even, midpoint between middle 2 values | ‐ |\n| Mode | ‐ | Value which repeats most often (its possible to have zero or multiple modes) | ‐ |\n| Range | R | Max(Xi )– Min(Xi ) | ‐ |\n| Variance | s2 | ∑~~ ~~௑௡~~ ~~మ~~ ~~ for population 􀁖 2, divide by n | 􀁖 2 |\n| Standard Deviation | s | Sqrt(s2 ) | 􀁖 |\n\nPg. 63, Reference book ver. 10  \nOthers: Coefficient of variation (CV), geometric mean, root mean square (RMS)  \nExamples  \nWhat is the sample variance of the following numbers?  \n2,4,6,8,10,12,14  \na) 4.32  \nb) 5.29  \nc) 8.00  \nd) 18.70 SOLN:  \nത ∑ ௑ ೔ ଶାସା଺ା଼ାଵ଴ାଵଶାଵସ  \nFirst find mean: 􀜺 ൌ ~~ ~~௡~~ ~~ ൌ  ଻  ൌ 8  \nThen S2 = ∑ ௑ ೔  మ ൌ  ଶି଼ మ ା ସି଼ మ ା ଺ି଼ మ ା ଼ି଼ మ ା ଵ଴ି଼ మ ା ଵଶି଼ మ ା ଵସି଼ మ ൌ 18.67 (d)௡ିଵ ଻ିଵ  \nDouble checks: should be positive! Asking for S or S2 ? Or 􀁖 or 􀁖2 ?  \nWhat is the median of the following data? 10, 7, 12, 4, 6, 8  \na) 4  \nb) 7.5  \nc) 8  \nd) 10 SOLN:  \nPut in ascending (sort) order: 4,6,7,8,10,12  \nIf n odd, middle item; if even, average of middle two items m = (7+8) / 2 = 7.5 (b)  \nFollow‐up: What is the mode of this data?  \nConfidence Intervals  \nത  \nProvide a bracket on the location of the true population mean given a sample 􀜺 and S. Based on Student‐T distribution  \nത ௌ ത ௌ  \n◦ If standard deviation 􀁖 is unknown: 􀜺 െ 􀝐~~ ~~ഀమ,௡ିଵ ~~ ~~௡ ൏ 􀟤 ൏ 􀜺 ൅􀝐~~ ~~ഀమ,௡ିଵ Standard error  \nത ఙ ത ఙ  \n◦ If standard deviation 􀁖 is known: 􀜺 െ 􀜼ఈ/ଶ~~ ~~௡ ൏ 􀟤 ൏ 􀜺 ൅􀜼 ఈ/ଶ~~ ~~௡  \nത ௌ  \nMay also be stated as: 􀜺 േ 􀝐 ఈ/ଶ ~~ ~~௡  Half width  \n􀁄 =significance level (type 1 error) = 1 – confidence level  \nZ values: use table on page 44, t‐values: use student‐t table pg. 46  \nIEs: also refresh on formulas for CI on difference means and on variance  \nPg. 74, Reference book ver. 10  \nExamples  \nYou collect 10 observations from an experiment. The sample average is 14.0, and the standard deviation is 5.8. The 90% confidence interval on the mean is:  \naሻ 11.57 ൏ μ ൏ 16.43 bሻ 10.68 ൏ μ ൏ 17.32 cሻ 8.2 ൏ μ ൏ 19.8 dሻ 8.78 ൏ μ ൏ 19.22  \nSOLN:  \nത  \nIdentify what you have: n=10, 􀜺 = 14.0, S=5 .8, confidence=0 .9 and population variance 􀁖 unknown  \nUse t, not Z. 􀁄 = 1 – 0.9 = 0.","cbCaicTcIF1B8JhN","https://ap.wps.com/l/cbCaicTcIF1B8JhN","pdf",1601834,66,"English","# Statistics Topics on FE\n## Number of questions by subject\n## Probability, expectations, and distributions\n## Regression and goodness of fit\n## Sampling, hypothesis testing, and error types\n## Analysis of Variance (ANOVA) and factorial design\n## Definitions: population, sample, parameter, statistic\n## Measures of central tendencies and dispersions\n## Confidence intervals: mean with t and Z\n## Worked examples and calculations","[{\"question\":\"What statistical topics are covered in the FE review for statistics?\",\"answer\":\"The review covers central tendency and dispersion, measures of uncertainty, confidence intervals, probability laws and distributions, expected value, regression and goodness of fit, sampling and hypothesis testing, and ANOVA/factorial design.\"},{\"question\":\"How are population, sample, parameter, and statistic defined in the document?\",\"answer\":\"Population is the full collection of measurements of interest, a sample is a subset extracted from the population, a parameter is a characteristic of the population, and a statistic is a characteristic of the sample.\"},{\"question\":\"How do you choose between Student-t and Z when computing confidence intervals for the mean?\",\"answer\":\"Use Student-t when the standard deviation is unknown, and use Z when the standard deviation (variance) is known, as shown in the worked examples.\"}]","FE Review - Statistics | PDF",166]