{"id":663,"date":"2025-05-08T07:25:25","date_gmt":"2025-05-08T07:25:25","guid":{"rendered":"https:\/\/yaveni.com\/blog\/?p=663"},"modified":"2025-05-08T07:25:26","modified_gmt":"2025-05-08T07:25:26","slug":"michael-records-the-number-of-miles-he-runs-each-week-for-nine-weeks","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/michael-records-the-number-of-miles-he-runs-each-week-for-nine-weeks\/","title":{"rendered":"Michael records the number of miles he runs each week for nine weeks"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Michael records the number of miles he runs each week for nine weeks. 6, 11, 13, 8, 15, 9, 11, 5, 9 Which box plot represents the data?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine which box plot represents Michael\u2019s weekly mileage data, we must calculate the five-number summary, which includes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Minimum<\/strong><\/li>\n\n\n\n<li><strong>First Quartile (Q1)<\/strong><\/li>\n\n\n\n<li><strong>Median (Q2)<\/strong><\/li>\n\n\n\n<li><strong>Third Quartile (Q3)<\/strong><\/li>\n\n\n\n<li><strong>Maximum<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Arrange the data in ascending order<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><code>5, 6, 8, 9, 9, 11, 11, 13, 15<\/code><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Identify the five-number summary<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Minimum:<\/strong> 5<\/li>\n\n\n\n<li><strong>Maximum:<\/strong> 15<\/li>\n\n\n\n<li><strong>Median (Q2):<\/strong> The middle value is the 5th number: <strong>9<\/strong><\/li>\n\n\n\n<li><strong>Lower Half:<\/strong> 5, 6, 8, 9<\/li>\n\n\n\n<li>Q1 (Median of lower half): (6 + 8)\/2 = <strong>7<\/strong><\/li>\n\n\n\n<li><strong>Upper Half:<\/strong> 11, 11, 13, 15<\/li>\n\n\n\n<li>Q3 (Median of upper half): (11 + 13)\/2 = <strong>12<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Final Five-Number Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Minimum: <strong>5<\/strong><\/li>\n\n\n\n<li>Q1: <strong>7<\/strong><\/li>\n\n\n\n<li>Median (Q2): <strong>9<\/strong><\/li>\n\n\n\n<li>Q3: <strong>12<\/strong><\/li>\n\n\n\n<li>Maximum: <strong>15<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">What should the box plot look like?<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>The left whisker<\/strong> extends from <strong>5 to 7<\/strong><\/li>\n\n\n\n<li><strong>The box<\/strong> goes from <strong>7 to 12<\/strong>, with a line at <strong>9<\/strong> (the median)<\/li>\n\n\n\n<li><strong>The right whisker<\/strong> extends from <strong>12 to 15<\/strong><\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A box plot, also called a box-and-whisker plot, graphically represents the distribution of a data set. It shows central tendency and variability without displaying all individual data points.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>box<\/strong> represents the interquartile range (IQR), which contains the middle 50% of the data (from Q1 to Q3).<\/li>\n\n\n\n<li>The <strong>line inside the box<\/strong> is the <strong>median<\/strong>, showing the data&#8217;s center.<\/li>\n\n\n\n<li>The <strong>whiskers<\/strong> extend from the box to the minimum and maximum values, showing the full data range.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This plot helps detect skewness and outliers. In this case, the data are fairly symmetric, and no extreme outliers exist.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The correct box plot will have:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Whiskers at <strong>5<\/strong> and <strong>15<\/strong><\/li>\n\n\n\n<li>Box from <strong>7<\/strong> to <strong>12<\/strong><\/li>\n\n\n\n<li>Line at <strong>9<\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Michael records the number of miles he runs each week for nine weeks. 6, 11, 13, 8, 15, 9, 11, 5, 9 Which box plot represents the data? The correct answer and explanation is : To determine which box plot represents Michael\u2019s weekly mileage data, we must calculate the five-number summary, which includes: Step 1: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-663","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/663","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=663"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/663\/revisions"}],"predecessor-version":[{"id":664,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/663\/revisions\/664"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=663"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=663"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}