[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-490191-en":3,"detail-sidebar-cat-0-en-105":30,"doc-seo-490191-105":80},{"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":11,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29,"preview_page_count":4},490191,7971478544854,"miaandmiso","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",4,"Exam","Chapter - 5 - Descriptive Statistics","Chapter on descriptive statistics covering key definitions and how data are organized and summarized. Introduces population and sample, statistical variables and their modalities, then details quantitative versus qualitative variables with discrete/continuous and nominal/ordinal types. Explains organizing data through statistical series, absolute and relative frequencies, cumulative frequencies, and continuous variable class limits, amplitude, and class centers. Presents position parameters including mean and mode formulas for both discrete and grouped continuous cases, with worked examples and tables.","Chapter  \nDescriptive Statistics  \n4  \n4.1 Statistical Vocabulary  \n1. Population: is the set of individuals or objects of the same nature on which the study relates.  \nThe components of the population are called individuals, elements, or statistical units.  \n2. Sample: A subset of the population selected for study  \n3. Statistical Variable:The character X is the subject under statistical study.  \n4. Statistical Modality:The category or the different possible situations (levels) of a statistical variable.  \nExample 4.1.1 Scores of six students in a statistics test can be 4 , 6 , 8 , 3 , 2 and 9 marks.  \n• The variable is: marks.  \n• The modalities (values) are: 4 , 6 , 8 , 3 , 2 , 9.  \n4.1.1 Types of Statistical Variables  \nThere are two types of statistical variables  \n4.1.1.1 Quantitative Variables  \nQuantitative Variables are the variables that can be measured or give us numbers representing counts, or variables whose modalities are numbers.  \nMoreover the quantitative variables are divided into two main types distrete and continous.  \n1. Discrete : A variable is discrete if it takes isolated values (usually integers) . Example 4.1.2 • The number of children in a family (1 , 2 , 3) .  \n• The number of students in a classroom.  \n• The number of accidents in a city.  \n2. Continuous: A variable is continuous when it can take numbers from an interval of real numbers.  \nExample 4.1.3 • Temperature: For example, the temperature in Mila city last summer was between 15 and 56, i. e . , [15 , 56] .  \n4.1.1.2 Qualitative Variables  \nQualitative Variables are variables that are not measurable numerically. The qualitative variables can be  \n1. Nominal: Variables whose modalities cannot be ordered according to their meaning  \nExample 4.1.4 • Gender: male, female.  \n• Eye color: Black, Brown.  \n• Religion: Muslim, Christian.  \n2. Ordinal: Variables whose modalities are ordered according to their meaning (hierarchy) .  \nExample 4.1.5 • Grade: {A, B, C, D, E} .  \n• Rating scale: (bad, good, excellent) .  \n• Ranking of football players: (first grade, second grade, third grade) .  \n4.2 Organizing data  \n• Statistical Series:A statistical series is the simplest form of presenting statistical data.  \n• Absolute Frequency ni: The absolute frequency ni is the number of statistical elements corresponding to a given modality.  \n• Cumulative Absolute Frequency nci↑ : The cumulative absolute frequency nci↑ is the number of individuals corresponding to the same modality and all previous modalities.  \n• Relative Frequencyfi: The relative frequency is defined by fi = nNi ,  \nwhere N is the total number of observations.  \n• Cumulative Relative Frequency fic↑ : The cumulative relative frequency is defined by  \nfic↑ = nNc~~i~~↑ .  \nExample 4.2.1 The table below shows the number of children per family, with abso lute frequency (ni ), cumulative absolute frequency (Ni− ), relative frequency (fi), and cumulative relative frequency (Fi− ):  \n\n| Number of Children xi | ni | nci↑ | fi | fic↑ |\n| --- | --- | --- | --- | --- |\n| 0 | 16 | 16 | 0.250 | 0.250 |\n| 1 | 18 | 34 | 0.281 | 0.531 |\n| 2 | 14 | 48 | 0.218 | 0.749 |\n| 3 | 11 | 59 | 0.172 | 0.921 |\n| 4 | 3 | 62 | 0.047 | 0.968 |\n| 5 | 2 | 6 | 0.031 | 1.000 |\n| Total | 64 | − | 1.000 | − |\n\nContinuous Statistical Variables  \n• Class Limits: For each class, we define:  \n– a lower limit,  \n– an upper limit.  \n• Class Amplitude: The amplitude of a class is  \na = upper limit − lower limit.  \n• Class Center The center of a class is  \nci = lower~~ ~~limit~~ ~~+2~~ ~~upper~~ ~~limit .  \nExample 4.2.2 Suppose we record the daily study hours of 30 students. We group the  \ndata into classes and calculate class limits, class amplitude, and class centers.  \n\n| Class | Lower Limit | Upper Limit | Amplitude a | Class Center ci |\n| --- | --- | --- | --- | --- |\n| [0, 2[ | 0 | 2 | 2 | 1 |\n| [2, 4[ | 2 | 4 | 2 | 3 |\n| [4, 6[ | 4 | 6 | 2 | 5 |\n| [6, 8[ | 6 | 8 | 2 | 7 |\n| [8, 10[ | 8 | 10 | 2 | 9 |\n\n4.3 Position Parameters  \n4.","cbCaivGGQNz8J9YU","https://ap.wps.com/l/cbCaivGGQNz8J9YU","pdf",237782,1,12,"English","en",105,"# 4 Descriptive Statistics\n## 4.1 Statistical Vocabulary\n## 4.2 Organizing data\n## 4.3 Position Parameters","[{\"question\":\"What is the difference between a population and a sample in descriptive statistics?\",\"answer\":\"A population is the set of all individuals or objects related to the study. A sample is a subset of the population selected for the study.\"},{\"question\":\"How are quantitative variables and qualitative variables classified?\",\"answer\":\"Quantitative variables are measurable and their modalities are numbers; they are divided into discrete and continuous. Qualitative variables are not measurable numerically; they are divided into nominal and ordinal types.\"},{\"question\":\"How are the mean and mode calculated for discrete versus continuous/grouped data?\",\"answer\":\"For discrete variables, the mean uses the sum of xi weighted by their frequencies. For continuous grouped data, the mean uses class centers ci weighted by ni. The mode is the most frequent value for discrete variables, while for continuous variables it uses a modal-class-based formula involving class limits, neighboring frequencies, and class amplitude.\"}]","Chapter - 5 - Descriptive Statistics | PDF",1790833900,30,{"code":4,"msg":5,"data":31},[32,37,42,45,50,55,60,64,69,72,76],{"id":20,"doc_module":4,"doc_module_name":33,"category_name":34,"show_sort_weight":35,"slug":36},"Document","Story & Novel",90,"story-novel",{"id":38,"doc_module":4,"doc_module_name":33,"category_name":39,"show_sort_weight":40,"slug":41},2,"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":33,"category_name":12,"show_sort_weight":43,"slug":44},70,"exam",{"id":46,"doc_module":4,"doc_module_name":33,"category_name":47,"show_sort_weight":48,"slug":49},5,"Comic",60,"comic",{"id":51,"doc_module":4,"doc_module_name":33,"category_name":52,"show_sort_weight":53,"slug":54},6,"Technology",50,"technology",{"id":56,"doc_module":4,"doc_module_name":33,"category_name":57,"show_sort_weight":58,"slug":59},7,"Healthcare",40,"healthcare",{"id":61,"doc_module":4,"doc_module_name":33,"category_name":62,"show_sort_weight":29,"slug":63},8,"Research & Report","research-report",{"id":65,"doc_module":4,"doc_module_name":33,"category_name":66,"show_sort_weight":67,"slug":68},9,"Religion & Spirituality",20,"religion-spirituality",{"id":67,"doc_module":4,"doc_module_name":33,"category_name":70,"show_sort_weight":67,"slug":71},"World Cup","world-cup",{"id":73,"doc_module":4,"doc_module_name":33,"category_name":74,"show_sort_weight":73,"slug":75},10,"Lifestyle","lifestyle",{"id":77,"doc_module":4,"doc_module_name":33,"category_name":78,"show_sort_weight":46,"slug":79},19,"General","general",{"code":4,"msg":81,"data":82},"ok",{"site_id":24,"language":23,"slug":83,"title":13,"keywords":84,"description":14,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":144},"chapter-5-descriptive-statistics","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":33,"@type":93,"position":38},"https://docshare.wps.com/document/",{"item":97,"name":12,"@type":93,"position":98},"https://docshare.wps.com/document/exam/",3,{"item":100,"name":13,"@type":93,"position":11},"https://docshare.wps.com/document/chapter-5-descriptive-statistics/490191/",{"url":100,"name":13,"@type":102,"image":103,"author":108,"headline":13,"publisher":110,"fileFormat":113,"inLanguage":23,"description":14,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/chapter-5-descriptive-statistics/490191.png","ImageObject",300,407,{"name":9,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-10-25","2026-10-01",true,{"@type":118,"interactionType":119,"userInteractionCount":11},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"What is the difference between a population and a sample in descriptive statistics?","Question",{"text":128,"@type":129},"A population is the set of all individuals or objects related to the study. A sample is a subset of the population selected for the study.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"How are quantitative variables and qualitative variables classified?",{"text":133,"@type":129},"Quantitative variables are measurable and their modalities are numbers; they are divided into discrete and continuous. Qualitative variables are not measurable numerically; they are divided into nominal and ordinal types.",{"name":135,"@type":126,"acceptedAnswer":136},"How are the mean and mode calculated for discrete versus continuous/grouped data?",{"text":137,"@type":129},"For discrete variables, the mean uses the sum of xi weighted by their frequencies. For continuous grouped data, the mean uses class centers ci weighted by ni. The mode is the most frequent value for discrete variables, while for continuous variables it uses a modal-class-based formula involving class limits, neighboring frequencies, and class amplitude.","https://schema.org",{"og:url":100,"og:type":140,"og:title":13,"og:site_name":111,"og:description":14},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":7,"site_id":24},1791741854]