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A phenomenographic research approach was used with an adapted task as the data collection instrument, followed by clinical interviews with 20 students from each grade level. Analysis was conducted using an analysis-framework hierarchy of development for variability. Findings indicate most students reached Level 1 or Level 0, while Levels 3 and 4 were less common and mainly represented by 3rd and 4th graders. Overall, one in four students struggled with such inferences.",{"@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":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/informal-statistical-inferences-of-primary-school-students-on-the-concept-of-variability/588272/",{"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/informal-statistical-inferences-of-primary-school-students-on-the-concept-of-variability/588272.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the study’s main purpose?","Question",{"text":112,"@type":113},"To reveal how primary school students make informal statistical inferences about the concept of variability.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How were the data collected?",{"text":117,"@type":113},"An adapted task served as a data collection tool, and clinical interviews were conducted with 20 students from each grade level.",{"name":119,"@type":110,"acceptedAnswer":120},"What were the key findings about students’ variability levels?",{"text":121,"@type":113},"Most students were concentrated at Level 1, followed by Level 0. Levels 3 and 4 involved fewer students, with no 1st grade student at Level 4 and most Level 3–4 students coming from 3rd and 4th grades.","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},588272,1792064888,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","INFORMAL STATISTICAL INFERENCES OF PRIMARY SCHOOL STUDENTS ON THE CONCEPT OF VARIABILITY  \nNadide YILMAZ, Sümeyye AKTAŞ  \nAbstract: It was aimed to reveal the informal statistical inferences of primary school students on the concept of variability. A phenomenographic research approach was adopted. A task was adapted and used as a data collection tool. Clinical interviews were conducted with 20 primary school students from each grade level. Data were analyzed within the context of the analysis framework hierarchy of development for variability. The results showed that the highest number of students were at Level 1, followed by those who are at Level 0. It can also be seen that the numbers of the students who are at Level 3 and Level 4 are close to each other and smaller than the number of students at Level 1. In addition, it is seen that there is no 1st grade student at Level 4 and that the majority of the students at Level 3 and Level 4 are 3rd and 4th graders. One out of four students had difficulty in informal statistical inferences on the concept of variability. Informal statistical inferences on the concept of variability of three out of every four students, albeit at different levels, drew attention.  \nKey words: primary school students, variability, informal statistical infereneces, task, clinical interviews  \n1. Introduction  \nThe fact that individuals encounter graphs, tables and probabilistic situations in all areas of life (Cobb & Moore, 1997) makes it necessary for them to understand and interpret these situations correctly (Watson, 2006) . This has made it necessary to include probability and statistics in the teaching process and for students to acquire the related knowledge and skills. However, the inclusion of statistics and probability in school mathematics has a relatively recent history (Watson, 2018) . National and international institutions (e.g., Franklin, et al., 2005; Ministry of National Education [MoNE], 2018; National Council of Mathematics [NCTM], 2000) aim to impart knowledge and skills related to statistics and probability concepts to students from an early age by enabling them “to understand basic concepts related to probability, to formulate questions that include data collection and analysis, to create, organize and explain the representations of data and to read and interpret data”. Researchers have argued over the relevance of various statistical concepts to early-age learners and they have mostly concluded that emerging teaching approaches often limit students’ opportunities to learn or that students are not ready to learn these subjects (English & Mulligan, 2013; Makar, 2018; Perry & Dockett, 2008) . When the curriculum in Turkey is examined, it is seen that it aimed to enable the primary school 1st-4th grade students “to read simple tables with at most two data groups, collect data for a given research question, represent and interpret the data with tables and object graphs, prepare a frequency table and tree diagram and read a figure graph, read and interpret simple tables with up to three data groups and organize the data obtained from the table and examine and create a bar graph”. In addition, it is aimed to make them use different representations to present the data they have obtained and to solve and pose problems related to daily life by using the information shown in tree diagrams, bar charts, tables and other graphs (MoNE, 2018; p. 14) . It can be said that, it is formally aimed to equip students with knowledge and skills related to various graphs and tables. However, the concepts of statistics and probability that students encounter in daily life are much more than these because it is possible to engage in statistical concepts more than it is thought in daily life (Paparistodemou & Meletiou-Mavrotheris, 2018) . One of these concepts is the concept of variability (Wild & Pfannkuch, 1999) . In this study, it is aimed to reveal the informal statistical inferences of primary school stu","cbCaijAVhrWsfkWR","https://ap.wps.com/l/cbCaijAVhrWsfkWR","pdf",401166,15,"English","# Introduction\n# Theoretical Framework\n## The concept of variability","[{\"question\":\"What is the study’s main purpose?\",\"answer\":\"To reveal how primary school students make informal statistical inferences about the concept of variability.\"},{\"question\":\"How were the data collected?\",\"answer\":\"An adapted task served as a data collection tool, and clinical interviews were conducted with 20 students from each grade level.\"},{\"question\":\"What were the key findings about students’ variability levels?\",\"answer\":\"Most students were concentrated at Level 1, followed by Level 0. Levels 3 and 4 involved fewer students, with no 1st grade student at Level 4 and most Level 3–4 students coming from 3rd and 4th grades.\"}]","INFORMAL STATISTICAL INFERENCES OF PRIMARY SCHOOL STUDENTS ON THE CONCEPT OF VARIABILITY | PDF",38]