{"id":471,"date":"2022-04-12T10:41:02","date_gmt":"2022-04-12T10:41:02","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=471"},"modified":"2024-08-21T02:29:15","modified_gmt":"2024-08-21T02:29:15","slug":"x-4-interpret-stem-and-leaf-plots","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/x-4-interpret-stem-and-leaf-plots\/","title":{"rendered":"X.4 Interpret stem-and-leaf plots"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Interpret stem-and-leaf plots<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#94bb2a\">1. <strong>Understanding a Stem-and-Leaf Plot<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Stem-and-Leaf Plot<\/strong>: A way to organize and display numerical data where each number is split into a &#8220;stem&#8221; (the leading digit(s)) and a &#8220;leaf&#8221; (the last digit).<\/li>\n\n\n\n<li><strong>Purpose<\/strong>: To quickly show the distribution of data and identify patterns like the median, mode, range, and outliers.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"226\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-9.png\" alt=\"\" class=\"wp-image-13763\"\/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#0ca1ab\">2. <strong>Components of a Stem-and-Leaf Plot<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Stem<\/strong>: Represents the leading digit(s) of each number. For example, in the number 47, the stem would be 4.<\/li>\n\n\n\n<li><strong>Leaf<\/strong>: Represents the last digit of each number. In the number 47, the leaf would be 7.<\/li>\n\n\n\n<li><strong>Key<\/strong>: A key is usually provided to explain how to read the plot. For example, &#8220;4 | 7 means 47.&#8221;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#351dcc\">3. <strong>Steps to Interpret a Stem-and-Leaf Plot<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1: Read the Key<\/strong>\n<ul class=\"wp-block-list\">\n<li>Start by understanding the key to know how to read the stems and leaves.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Step 2: Identify the Data Points<\/strong>\n<ul class=\"wp-block-list\">\n<li>Combine the stem and leaf to form the original numbers. For example, if the stem is 5 and the leaf is 3, the number is 53.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Step 3: Analyze the Distribution<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Range<\/strong>: Find the difference between the highest and lowest values by looking at the first and last numbers.<\/li>\n\n\n\n<li><strong>Median<\/strong>: Locate the middle value by counting from both ends of the list.<\/li>\n\n\n\n<li><strong>Mode<\/strong>: Identify the most frequent data point by observing which leaf appears most often.<\/li>\n\n\n\n<li><strong>Clusters and Gaps<\/strong>: Notice any clusters of data (where many numbers are close together) and gaps (where few or no numbers appear).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#ec0000\">4. <strong>Example of a Stem-and-Leaf Plot<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Data Set<\/strong>: 32, 34, 36, 41, 42, 43, 45, 47, 52, 53, 53, 54, 61.<\/li>\n\n\n\n<li><strong>Stem-and-Leaf Plot<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-1024x1024.png\" alt=\"\" class=\"wp-image-13765\" style=\"aspect-ratio:1;width:314px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-1024x1024.png 1024w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-768x768.png 768w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-400x400.png 400w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-1536x1536.png 1536w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1-1568x1568.png 1568w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/3-1.png 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Key<\/strong>: 3 | 2 means 32.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#a41c1c\">5. <strong>Analyzing the Example Plot<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Range<\/strong>: The range is 61 &#8211; 32 = 29.<\/li>\n\n\n\n<li><strong>Median<\/strong>: The middle value is the 7th number (45).<\/li>\n\n\n\n<li><strong>Mode<\/strong>: The number 53 appears most often.<\/li>\n\n\n\n<li><strong>Clusters<\/strong>: There\u2019s a cluster around 40-50.<\/li>\n\n\n\n<li><strong>Gaps<\/strong>: There is a gap between the leaf values from 6 to 1 in the stems 3 and 4.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#2738bb\">6. <strong>Benefits of Stem-and-Leaf Plots<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Detailed View<\/strong>: Shows individual data points while also providing a visual distribution.<\/li>\n\n\n\n<li><strong>Quick Analysis<\/strong>: Allows for rapid identification of key statistical concepts like median and mode.<\/li>\n\n\n\n<li><strong>Comparison<\/strong>: Makes it easier to compare different sets of data, especially in finding where data clusters.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#836f00\">7. <strong>Common Mistakes to Avoid<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Misinterpreting the Key<\/strong>: Always read the key correctly to avoid confusion between stems and leaves.<\/li>\n\n\n\n<li><strong>Forgetting to Order the Leaves<\/strong>: Leaves should be listed in ascending order for clarity.<\/li>\n\n\n\n<li><strong>Overlooking the Range and Gaps<\/strong>: Always check the full spread of data and note any significant gaps.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color\" style=\"color:#6f175f\">8. <strong>Practical Tips<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Practice reading different stem-and-leaf plots to get comfortable with the format.<\/li>\n\n\n\n<li>Pay attention to the shape of the distribution, as it can indicate the nature of the data set.<\/li>\n\n\n\n<li>Use stem-and-leaf plots to double-check calculations like median or mode.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-huge-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-large-font-size\" style=\"background-color:#ebb2e2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\ud83c\udf00 Jen counted the number of pieces of pepperoni on each pizza she made.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-21.png\" alt=\"\" class=\"wp-image-5341\" style=\"aspect-ratio:1;width:340px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-21.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-21-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-21-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-21-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>How many pizzas had fewer than 40 pieces of pepperoni?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">&nbsp;_______ pizzas<\/p>\n<\/div><\/div>\n\n\n\n<p>Count all the leaves in the rows with stems 1, 2, and 3.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-12.png\" alt=\"\" class=\"wp-image-5342\" style=\"aspect-ratio:1;width:345px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-12.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-12-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-12-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-12-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>You counted 11 leaves, which are blue in the stem-and-leaf plot above. 11 pizzas had fewer than 40 pieces of pepperoni.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-large-font-size\" style=\"background-color:#dcfbdb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\ud83c\udf00 Jada counted the pages in each book on her English class&#8217;s required reading list.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-8.png\" alt=\"\" class=\"wp-image-5343\" style=\"aspect-ratio:1;width:279px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-8.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-8-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-8-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-8-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>How many books had exactly 55 pages?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">________&nbsp;books<\/p>\n<\/div><\/div>\n\n\n\n<p>For the number 55, the stem is 5, and the leaf is 5. Find the row where the stem is 5. In that row, count all the leaves equal to 5.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-10.png\" alt=\"\" class=\"wp-image-5344\" style=\"aspect-ratio:1;width:314px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-10.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-10-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-10-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-10-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>You counted 4 leaves, which are blue in the stem-and-leaf plot above. 4 books had exactly 55 pages.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-large-font-size\" style=\"background-color:#dedbfa\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\ud83c\udf00 A volunteer for the local running club counted the number of participants at each race.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-5.png\" alt=\"\" class=\"wp-image-5345\" style=\"aspect-ratio:1;width:300px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-5.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-5-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-5-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-5-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>How many races had at least 20 participants but fewer than 60 participants?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">&nbsp;_____ races<\/p>\n<\/div><\/div>\n\n\n\n<p>Count all the leaves in the rows with stems 2, 3, 4, and 5.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9.png\" alt=\"\" class=\"wp-image-5346\" style=\"aspect-ratio:1;width:328px;height:auto\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>You counted 4 leaves, which are blue in the stem-and-leaf plot above. 4 races had at least 20 participants but fewer than 60 participants.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76707\/349\/775\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-144.png\" alt=\"\" class=\"wp-image-6932\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-144.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-144-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-144-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-144-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76760\/717\/932\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-146.png\" alt=\"\" class=\"wp-image-6933\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-146.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-146-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-146-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-146-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Interpret stem-and-leaf plots key notes : 1. Understanding a Stem-and-Leaf Plot 2. Components of a Stem-and-Leaf Plot 3. Steps to Interpret a Stem-and-Leaf Plot 4. Example of a Stem-and-Leaf Plot 5. Analyzing the Example Plot 6. Benefits of Stem-and-Leaf Plots 7. Common Mistakes to Avoid 8. Practical Tips Learn with an example \ud83c\udf00 Jen counted<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/x-4-interpret-stem-and-leaf-plots\/\">Continue reading <span class=\"screen-reader-text\">&#8220;X.4 Interpret stem-and-leaf plots&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"footnotes":""},"class_list":["post-471","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/471","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=471"}],"version-history":[{"count":17,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/471\/revisions"}],"predecessor-version":[{"id":13767,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/471\/revisions\/13767"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}