[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-315968-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-315968-en":130},{"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","unit-3-general-mathematics-statistics-summary-notes-data-analysis-univariate-statistics","UNIT 3 GENERAL MATHEMATICS STATISTICS SUMMARY NOTES - Data Analysis & Univariate Statistics","","A set of statistics study summary notes for Unit 3 general mathematics, focusing on data analysis and univariate statistics. It explains regression analysis steps, including listing EV and RV, entering data, constructing scatterplots, obtaining least-squares regression lines, and checking residuals for linearity. It then covers variable types (categorical and numerical), frequency tables, and multiple graphing methods such as bar charts, segmented bar charts, histograms, dot plots, and stem plots. Finally, it details median, range, interquartile range, five-number summaries, box plots, outlier detection, comparing distributions, measures of centre (mean vs median), and the normal distribution with the 68-96-99.7% rule and standard deviation.",{"@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/unit-3-general-mathematics-statistics-summary-notes-data-analysis-univariate-statistics/315968/",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/unit-3-general-mathematics-statistics-summary-notes-data-analysis-univariate-statistics/315968.png","ImageObject",300,407,{"name":42,"@type":43},"Patrick","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-07","2026-09-20",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",19,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are the steps to perform least-squares regression analysis in the notes?","Question",{"text":63,"@type":64},"List the EV and RV names, enter the data into lists, construct a scatterplot, find the least-squares regression line (Calc > Regression > Linear Reg), then write down key results and graph residuals against EV to test the linearity assumption.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do the notes distinguish categorical variables from numerical variables?",{"text":68,"@type":64},"Categorical variables represent characteristics and include nominal and ordinal types. Numerical variables represent quantities that can be counted or measured and include discrete and continuous types, with examples for each.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you determine outliers using the box-plot method in these notes?",{"text":72,"@type":64},"Compute outlier limits using 1.5 × IQR, then treat values beyond Q3 + (1.5 × IQR) or below Q1 − (1.5 × IQR) as outliers; the notes also show an example five-number summary.","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},315968,1790031752,{"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":55,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145,"preview_page_count":4},549758146520,"https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470","UNIT 3 GENERAL MATHEMATICS STATISTICS SUMMARY NOTES  \nWRITTEN BY A 99.95 STUDENT WHO OBTAINED A 47 STUDY SCORE  \nData Analysis  \nRegression Analysis  \n1. Write down the EV and RV names as the list names  \n2. Enter data into lists  \n3. Construct a scatterplot (Set Graph)  \n4. Find the Least squares regression line (Calc > Regression > Linear Reg)  \n5. Write down the key results and graph residuals against EV to test linearity assumption  \nUnivariate Data  \nCategorical Variables: represents characteristics or qualities of people or things  \n• Nominal: data values that can be used to groups individuals according to a characteristic Example. Eye Colour, Gender, Postal Code  \n• Ordinal: data values that can be used to both group and order individuals according to a characteristic  \nExample. Fitness Level, Economic Status, Education Level  \nNumerical Variables: represents quantities and things that can be counted or measured  \n• Discrete: represents quantities that are counted in exact values Example. Number of People, Pages in a book, Goals scored  \n• Continuous: represents quantities that are measured on a decimal scale Example. Weight, Temperature, Costs to fill a tank with petrol  \nFrequency Table  \n• A listing of values a variable takes in a dataset, along with how frequently each value occurs  \nExample:  \nThe sex of 11 preschool children is as shown (F = Female, M = Male):  \nF M M F F M F F F M M  \nBar Chart  \n• Represents key information in a frequency tables as picture, which has bars of equal width and spacing to represent each category  \n• Note: may be frequency or percentage frequency  \nExample:  \nThe climate type of 23 countries is classified as ‘cold’, ‘mild’, or ‘hot’. Construct a frequency bar chart to display this information using the data summarised in the table.  \nSegmented Bar Chart  \n• Bars that are stacked on top of one another to give a single bar with several segments, with the length of each being the frequency  \n• Legend is required to identify categories  \nHistograms  \n• A graphical display of information in a grouped frequency table with bars of equal width and no spacing  \nExample:  \nConstruct a histogram for the frequency table.  \nDot Plots  \n• Displays discrete numerical data for small data sets  \nExample:  \nThe ages (in years) of the 13 members of a cricket team are:  \n22 19 18 19 23 25 22 29 18 22 23 24 22  \nStem Plots  \n• Displays discrete and continuous data for small to medium sized data sets  \nExample:  \nUniversity participation rates (%) in 23 countries are given below.  \n26 3 12 20 36 1 25 26 13 9 26 27 15 21 7 8 22 3 37 17 55 30 1  \nWhich graph?  \n\n| Categorical | Bar chart | 5-10 categories |\n| --- | --- | --- |\n|  | Segmented bar chart | Not too many categories (maximum 4-5) |\n\n\n| Numerical | Histogram | Medium – large data sets (n ≥ 40) |\n| --- | --- | --- |\n|  | Stem plot | Small – medium data sets (n ≤ 50) |\n|  | Dot plot | Small data sets (n ≤ 20) |\n\nMedian, Range and Interquartile Range  \nMedian: middle value of the ordered data set  \n• Located at the 􁉀􀯡~~ ~~+21􁉁 􀝐ℎ position, where n = number of data values  \n• Measure of centre of a distribution  \nRange: difference between the largest and smallest value in the data set  \n• R = largest data value – smallest data value  \n• Measure of spread of a distribution, the maximum spread of the data values  \nInterquartile Range: the spread of the middle of the 50% of data values  \n• IQR = 􀜳3 − 􀜳 1  \n`` Q1 is the midpoint of the lower half of the data values Q2 is the median  \nQ3 is the midpoint of the upper half of the data values  \nChoosing the best measure of the centre of distribution  \n• Symmetric Distribution w/ no outliers >>> Range or IQR  \n• Skewed and/or outliers >>> IQR  \nFive Number Summary:  \nminimum, Q1, median, Q3, maximum  \n* Includes outliers *  \nBox Plots  \n• A graphical display of a five-number summary  \n• Note: label the number line and box plot  \nOutliers: 􀜳 3 + (1.5 × 􀜫􀜳􀜴) 􀝋􀝎 􀜳 1 − (1.5 × 􀜫􀜳􀜴)  \nExample:  \nConstruct a box plot","cbCaipwKWESswntO","https://ap.wps.com/l/cbCaipwKWESswntO","pdf",4454249,35,"English","# Data Analysis\n## Regression Analysis\n# Univariate Data\n## Categorical and Numerical Variables\n## Frequency Tables and Graphs\n### Bar Charts and Segmented Bar Charts\n### Histograms, Dot Plots, Stem Plots\n# Median, Range, and Interquartile Range\n## Five-Number Summary and Box Plots\n## Outliers and Skewness\n# Comparing Distributions and Measures of Centre\n## Mean vs Median\n# Normal Distribution and Standard Deviation","[{\"question\":\"What are the steps to perform least-squares regression analysis in the notes?\",\"answer\":\"List the EV and RV names, enter the data into lists, construct a scatterplot, find the least-squares regression line (Calc \\u003e Regression \\u003e Linear Reg), then write down key results and graph residuals against EV to test the linearity assumption.\"},{\"question\":\"How do the notes distinguish categorical variables from numerical variables?\",\"answer\":\"Categorical variables represent characteristics and include nominal and ordinal types. Numerical variables represent quantities that can be counted or measured and include discrete and continuous types, with examples for each.\"},{\"question\":\"How do you determine outliers using the box-plot method in these notes?\",\"answer\":\"Compute outlier limits using 1.5 × IQR, then treat values beyond Q3 + (1.5 × IQR) or below Q1 − (1.5 × IQR) as outliers; the notes also show an example five-number summary.\"}]","UNIT 3 GENERAL MATHEMATICS STATISTICS SUMMARY NOTES - Data Analysis & Univariate Statistics | PDF",1789908631,88]