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It explains the difference between qualitative and quantitative data, including discrete versus continuous quantitative measurements, and introduces four sampling methods: simple random, stratified, cluster, and systematic sampling. It then covers descriptive statistics through measures of center (mean, median, mode) and measures of spread (range, quartiles, IQR, variance, standard deviation). Finally, it defines outliers using the 1.5 IQR rule and applies it to a sample dataset.",{"@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/statistics-concepts-vocab-introduction-to-statistics-measures-of-center-spread-and-outliers/490182/",{"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/statistics-concepts-vocab-introduction-to-statistics-measures-of-center-spread-and-outliers/490182.png","ImageObject",300,407,{"name":92,"@type":93},"cksankcs","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-10-01",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the difference between qualitative and quantitative data?","Question",{"text":112,"@type":113},"Qualitative data is descriptive information that describes something. Quantitative data is numerical information (numbers), which can be discrete (counted) or continuous (measured).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are the four main types of sampling?",{"text":117,"@type":113},"The four types are simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Each differs in how the population is divided and how observations are selected.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you determine whether a value is an outlier?",{"text":121,"@type":113},"A value is an outlier if it lies more than 1.5 IQRs below Q1 or above Q3. Using Q1 and Q3 from the dataset, compute the thresholds and check whether the value falls outside them.","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},490182,1791482008,{"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":39,"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":144,"read_time":145,"preview_page_count":4},3985747882755,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Statistics Concepts & Vocab  \nUpdated September 2020  \nIntroduction to Statistics  \nTypes of Data  \nData can be qualitative or quantitative.  \n● Qualitative data is descriptive information (it describes something)  \n● Quantitative data is numerical information (numbers)  \na. Quantitative data can be discrete or continuous. Discrete data is counted, continuous data is measured.  \nExample: What do we know about this cat?  \nQualitative:  \n● He is grey and white Quantitative:  \n● Discrete:  \n● He has 4 legs  \n● He has 2 eyes  \n● Continuous:  \n● He weighs 2.2 lb  \n● He is 8 inches tall  \nSampling  \nA population includes all of the elements from a set of data. A sample consists one or more observations drawn from the population. There are four main types of sampling:  \n● Simple random sampling-All individuals are equally likely to be chosen for the sample  \n● Stratified sampling-The population is divided into groups, then a simple random sample is chosen from each group  \n● Cluster sampling-The population is divided into groups , and a number of clusters are chosen at random. All individuals in those clusters are chosen for the sample  \n● Systematic sampling-A list is created of every member of the population. From the list, we randomly select every nth element from the list  \nDescriptive Statistics:  \nRepresenting data numerically  \nMeasures of center  \nMeasures of center use data points to approximate and understand a“middle value” or “average” of a given data set. The three most commonly used measures of center are the mean, median , and mode.  \nThe mean is also known as the average. To find the mean, we add all values, and divide by the number of values.  \nTo find the median, place the numbers in value order and find the middle.  \nThe mode is the number that occurs the most often.  \nExample data set: 3, 3, 4, 5, 6, 7, 8  \nMean:  =  \nMedian: 3, 3, 4, 5, 6, 7, 8  \nMode: 3  \n=  \nMeasures of spread  \nMeasures of spread of are used to describe the variability of a data set. The most commonly used measures of spread are the range, quartiles , variance, and standard deviation.  \nThe range is the difference between the highest and the lowest values in a data set. Quartiles divide the data into four equal groups. The first quartile (Q1) is the median of the lower half of the dataset. The third quartile (Q3) is the median of the upper half of the data set. The median is also known as the second quartile: it perfectly splits the data in half.  \nThe interquartile range (IQR) is the difference between Q3 and Q1 .  \nExample data set: 3, 3, 4, 5, 6, 7, 8  \nRange: 8-3 = 5  \nQ1: 3, 3, 4, 5, 6, 7, 8 (Remember, the median is 5, and Q1 is the median of the lower half. The lower half here is 3, 3, 4)  \nQ3: 3, 3, 4, 5, 6, 7, 8 (Remember, the median is 5, and Q3 is the median of the upper half. The upper half here is 6, 7, 8)  \nInterquartile range = Q3-Q1 = 7-3 = 4   \nMeasures of spread  \nFinding outliers  \nAn outlier is a data point that is an abnormal distance from other points. In other words, it is data that lies outside the other values in the set.  \nAn outlier is any data point that is over 1.5 IQRs below the first quartile (Q1) or above the third quartile (Q3) .  \nExample data set: 3, 10, 14, 19, 22, 29, 32, 36, 49, 70. Are there any outliers?  \nAn outlier would be any number lower than Q1-1. 5*IQR or higher than Q3 + 1. 5*IQR.  \nAny number in our dataset that is below-19 or above 69 is an outlier. Therefore, 70 is an outlier.","cbCaieg3LU8YCCnx","https://ap.wps.com/l/cbCaieg3LU8YCCnx","pdf",2220430,54,"English","# Introduction to Statistics\n## Types of Data\n## Sampling\n## Descriptive Statistics\n## Measures of Center\n## Measures of Spread\n## Finding outliers","[{\"question\":\"What is the difference between qualitative and quantitative data?\",\"answer\":\"Qualitative data is descriptive information that describes something. Quantitative data is numerical information (numbers), which can be discrete (counted) or continuous (measured).\"},{\"question\":\"What are the four main types of sampling?\",\"answer\":\"The four types are simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Each differs in how the population is divided and how observations are selected.\"},{\"question\":\"How do you determine whether a value is an outlier?\",\"answer\":\"A value is an outlier if it lies more than 1.5 IQRs below Q1 or above Q3. Using Q1 and Q3 from the dataset, compute the thresholds and check whether the value falls outside them.\"}]","Statistics Concepts & Vocab - Introduction to Statistics - Measures of Center, Spread, and Outliers | PDF",1790833880,136]