[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-160419-en":3,"doc-seo-160419-105":31,"detail-sidebar-cat-0-en-105":91},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},160419,962084925636,"Sophia Brooks","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",4,"Exam","4 Solutions to Exercises - About these solutions","Exercise solutions prepared by Darryl K. Nester provide guidance for grading and interpreting answers, including notes on possible errors and where to report feedback. The document explains how to use a table of random digits while accounting for variations in start position, label length, label assignment, and label placement across rows or columns. It also discusses using statistical software and calculators, covering standard deviations, quartiles with five-number summaries, and boxplot conventions.","4 Solutions to Exercises  \n4.1 About these solutions  \nThe solutions that follow were prepared by Darryl K. Nester. I occasionally pillaged or plagiarized solutions from the second edition (prepared by George McCabe), but I take full responsibility for any errors that may remain. Should you discover any errors or have any comments about these solutions (or the odd answers, in the back of the text), please report them to me:  \nDarryl Nester  \nBluffton College  \nBluffton, Ohio 45817  \nemail: [nesterd@bluffton. edu](nesterd@bluffton. edu)  \n[WWW:](WWW:) [http://www. bluffton. edu/](http://www. bluffton. edu/)~nesterd  \n4.2 Using the table of random digits  \nGrading SRSs chosen from the table of random digits is complicated by the fact that students can find some creative ways to (mis)use the table. Some approaches are not mistakes, but may lead to different students having different “right” answers. Correct answers will vary based on:  \n² The line in the table on which they begin (you may want to specify one if the text does not) .  \n² Whether they start with, e.g., 00 or 01 .  \n² Whether or not they assign multiple labels to each unit.  \n² Whether they assign labels across the rows or down the columns (nearly all lists in the text are alphabetized down the columns) .  \nSome approaches can potentially lead to wrong answers. Mistakes to watch out for include:  \n² They may forget that all labels must be the same length, e.g., assigning labels like 0 ; 1 ; 2 ;:::; 9 ; 10 ;::: rather than 00 ; 01 ; 02 ;::: .  \n² In assigning multiple labels, they may not give the same number of labels to all units. E.g., if there are 30 units, they may try to use up all the two-digit numbers, thus assigning 4 labels to the first ten units and only 3 to the remaining twenty.  \n4.3 Using statistical software  \nThe use of computer software or a calculator is a must for all but the most cursory treatment of the material in this text. Be aware of the following considerations:  \nAcknowledgments 51  \n² Standard deviations: Students may easily get confused by software which gives both  \nthe so-called “sample standard deviation”(the one used in the text) and the “population standarusuallydgdeviveniaao“ns”” a(dnividing byd the latter  a¾te(r thasigm) ,nb¡ut t1h. dSymbolicallyistinction is no, tte formelways clisar For example, many computer spreadsheets have a command such as “STDEV(::: )” to compute a standard deviation, but you may need to check the manual to find out which kind it is.  \nAs a quick check: for the numbers 1, 2, 3, s D 1 while ¾ D: 0:8165 . In general, if two values are given, the larger one is s and the smaller is ¾ . If only one value is given, and it is the “wrong” one, use the relationship s D ¾ q ~~n n~~¡~~1~~ .  \n² Quartiles and five-number summaries: Methods of computing quartiles vary between different packages. Some use the approach given in the text (that is, Q 1 is the median of all the numbers below the location of the overall median, etc.), while others use amore complicated approach. For the numbers 1, 2, 3, 4, for example, we would have Q 1 D 1:5 and Q 3 D 2:5, but Minitab reports these as 1.25 and 2.75, respectively.  \nSince I used Minitab for most of the analysis in these solutions, this was sometimes a problem. However, I remedied the situation by writing a Minitab macro to compute quartiles the IPS way. (In effect, I was “dumbing down” Minitab, since its method is more sophisticated.) This and other macros are available at my website.  \n² Boxplots: Some programs which draw boxplots use the convention that the “whiskers”extend to the lower and upper deciles (the 10th and 90th percentiles) rather than to the minimum and maximum. (DeltaGraph, which I used for most of the graphs in these solutions, is one such program. It took some trickery on my part to convince it to make them as I wanted them.)  \nWhile the decile method is merely different from that given in the text, some methods are (in my opinion) just plain wrong. Some graphi","cbCaihLQEaJ4GoW2","https://ap.wps.com/l/cbCaihLQEaJ4GoW2","pdf",1375600,2,1,243,"English","en",105,"# 4 Solutions to Exercises\n## 4.1 About these solutions\n## 4.2 Using the table of random digits\n## 4.3 Using statistical software\n## 4.4 Acknowledgments\n## 1 Chapter 1 Looking at Data — Distributions\n## Chapter 1 Solutions","[{\"question\":\"Who prepared these solutions and how can errors be reported?\",\"answer\":\"Darryl K. Nester prepared the solutions and provides contact details to report errors or comments about the answers. He notes responsibility for any remaining mistakes.\"},{\"question\":\"Why is grading based on a table of random digits complicated?\",\"answer\":\"Students can misuse the table in creative ways, and correct answers may vary depending on the starting line, the initial digits (e.g., 00 vs 01), whether multiple labels are assigned, and whether labels run across rows or down columns.\"},{\"question\":\"What software-related considerations are emphasized in the solutions?\",\"answer\":\"The text stresses checking what a program computes for sample vs population standard deviation, differences in quartile methods across packages, and boxplot whisker conventions (e.g., deciles vs min/max) as implementations may diverge from the book’s approach.\"}]","4 Solutions to Exercises - About these solutions | PDF",1788063198,612,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":29},"4-solutions-to-exercises-about-these-solutions","",{"@graph":37,"@context":85},[38,53,68],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,48,51],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":20},"https://docshare.wps.com/document/","Document",{"item":49,"name":12,"@type":44,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":44,"position":11},"https://docshare.wps.com/document/4-solutions-to-exercises-about-these-solutions/160419/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":42,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-04","2026-08-30",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Who prepared these solutions and how can errors be reported?","Question",{"text":75,"@type":76},"Darryl K. Nester prepared the solutions and provides contact details to report errors or comments about the answers. He notes responsibility for any remaining mistakes.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is grading based on a table of random digits complicated?",{"text":80,"@type":76},"Students can misuse the table in creative ways, and correct answers may vary depending on the starting line, the initial digits (e.g., 00 vs 01), whether multiple labels are assigned, and whether labels run across rows or down columns.",{"name":82,"@type":73,"acceptedAnswer":83},"What software-related considerations are emphasized in the solutions?",{"text":84,"@type":76},"The text stresses checking what a program computes for sample vs population standard deviation, differences in quartile methods across packages, and boxplot whisker conventions (e.g., deciles vs min/max) as implementations may diverge from the book’s approach.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,104,109,114,119,124,129,132,136],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":102,"slug":103},70,"exam",{"id":105,"doc_module":4,"doc_module_name":47,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":47,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":47,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":120,"doc_module":4,"doc_module_name":47,"category_name":121,"show_sort_weight":122,"slug":123},8,"Research & Report",30,"research-report",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":105,"slug":139},19,"General","general"]