[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-538032-105":59,"doc-detail-538032-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","mathematics-high-school-statistics-probability-theory-of-action-performance-level-descriptors-and-proficiency","MATHEMATICS HIGH SCHOOL STATISTICS & PROBABILITY - Theory of Action, Performance Level Descriptors, and Proficiency","","Mathematics high school standards focus on how students demonstrate knowledge, skills, and understanding through state assessments and common measures. Performance level descriptors connect assessment results to classroom instruction and formative systems, clarifying proficiency as a range of observable behaviors with multiple pathways. The material details how proficiency and task difficulty interact through text complexity, stimuli, and contexts, and then outlines expectations for statistics and probability, including descriptive statistics, modeling, regression, correlation vs. causation, conditional probability, and inference from randomized processes.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mathematics-high-school-statistics-probability-theory-of-action-performance-level-descriptors-and-proficiency/538032/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mathematics-high-school-statistics-probability-theory-of-action-performance-level-descriptors-and-proficiency/538032.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-10",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do performance level descriptors link state assessments to classroom instruction?","Question",{"text":112,"@type":113},"They bridge the state assessment to classroom instruction and local formative assessment systems by defining proficiency as observable student performance characteristics across a range.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What factors influence a student’s ability to demonstrate proficiency?",{"text":117,"@type":113},"Proficiency is influenced by text or stimulus complexity, the tasks students must complete, and the contexts in which they are engaged.",{"name":119,"@type":110,"acceptedAnswer":120},"Which skills are emphasized in statistics and probability at different proficiency levels?",{"text":121,"@type":113},"Students progress from arranging data, identifying histograms and outliers, and computing descriptive measures to creating box plots and histograms, comparing shape/center/spread, modeling data, using z-scores, and making inferences from randomized processes.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},538032,1791732116,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","MATHEMATICS HIGH SCHOOL STATISTICS & PROBABILITY  \nTheory of Action: Academic standards represent a collective commitment around what students should learn each year. The state assessment asks students to demonstrate their knowledge, skills, and understanding related to these standards using a common measure. The resulting data allows us to see patterns in performance that should guide school and district improvement, helping identify areas of strength and opportunity.  \nRole of Performance Level Descriptors in Defining Proficiency: Performance level descriptors bridge the state assessment to classroom instruction and the systems of formative assessments that guide local instruction and choices about individual students. Academic proficiency represents a range of observable student performance characteristics. There are multiple pathways to proficiency, and students rely upon their strengths differently within that range of performance.  \nProficiency and Difficulty: A student’s ability to demonstrate proficiency is influenced by the complexity of the texts or stimuli presented, tasks they’re asked to complete, and the contexts in which they are engaged. As student performance improves, students are typically able to handle more challenging texts/stimuli, tasks, and contexts, and are able to demonstrate their skills and knowledge more accurately and consistently.  \n\n| Statistics & Probability Student performance indicates the ability to… |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n| Claim 1 | Below Proficient | Approaching Proficient | Proficient |  | Above Proficient |\n| ID.1-4 | Arrange data points in ascending order.\u003Cbr>Given a data set, identify an appropriate histogram as related to the type of modes--unimodal, bimodal, multimodal.\u003Cbr>Identify possible outliers of a data set if present. | Identify descriptive statistics for center (such as mean, median, and mode) and spread (such as IQR and standard deviation) .\u003Cbr>Calculate the median for skewed data or mean for roughly symmetric data based on the shape.\u003Cbr>Given a box plot, identify possible outliers in the data set. |  | Create box plots with raw data.\u003Cbr>Create histograms with raw data.\u003Cbr>Given a set of raw data, describe the shape (e.g., skewed left/right or symmetric) .\u003Cbr>Identify appropriate methods to describe the center (median vs mean) and spread (IQR vs standard deviation) based on the shape of the given data.\u003Cbr>Determine when to retain or remove outliers based on the context of the problem. | In a real-world situation, compare the difference in spread for two different\u003Cbr>types of data sets--skewed vs.\u003Cbr>symmetric.\u003Cbr>In a real-world situation, compare shape, center, and spread when outliers are removed to the original shape, center, and spread with the outliers.\u003Cbr>In a real-world situation, determine an appropriate type of model and justify the decision.\u003Cbr>Calculate the z-score when given the mean, standard deviation, and data point.\u003Cbr>In a real-world situation, utilize the area under the normal curve to determine the z-score or vice versa. |\n\nID.5 Given sample spaces, interpret and calculate one-variable probabilities.  \nDetermine missing pieces of information from a two-way frequency table.  \nRepresent and interpret relative frequencies in context.  \nUse conditional probabilities to determine if two events are independent or dependent.  \n\n| Claim 1 | Below Proficient | Approaching Proficient | Proficient | Above Proficient |\n| --- | --- | --- | --- | --- |\n| ID.5 |  | Correctly identify the given population for a conditional probability statement. For example, find the probability that a bat tests positive for rabies, given it was active during the day. | Calculate conditional probabilities given a completed two-way table. |  |\n| ID.6-9 | Given a scatter plot, visually estimate an appropriate linear model.\u003Cbr>Visually Identify linear relationships as positive or negative correlations. | Use technology to calculate a linear regression for a ","cbCaipDjlXu3ByEy","https://ap.wps.com/l/cbCaipDjlXu3ByEy","pdf",223467,"English","# Theory of Action\n# Role of Performance Level Descriptors in Defining Proficiency\n# Proficiency and Difficulty\n# Statistics & Probability Student Performance Levels\n## Statistics and Probability: Claim ID.1-4, ID.5\n## Regression, Correlation, and Causation: ID.6-9\n## Statistical Experiments and Inference: IC.1-6","[{\"question\":\"How do performance level descriptors link state assessments to classroom instruction?\",\"answer\":\"They bridge the state assessment to classroom instruction and local formative assessment systems by defining proficiency as observable student performance characteristics across a range.\"},{\"question\":\"What factors influence a student’s ability to demonstrate proficiency?\",\"answer\":\"Proficiency is influenced by text or stimulus complexity, the tasks students must complete, and the contexts in which they are engaged.\"},{\"question\":\"Which skills are emphasized in statistics and probability at different proficiency levels?\",\"answer\":\"Students progress from arranging data, identifying histograms and outliers, and computing descriptive measures to creating box plots and histograms, comparing shape/center/spread, modeling data, using z-scores, and making inferences from randomized processes. \"}]","MATHEMATICS HIGH SCHOOL STATISTICS & PROBABILITY - Theory of Action, Performance Level Descriptors, and Proficiency | PDF",1791606026]